solutions of second order differential equations

... the possible values of the limits of y and of Δy Solutions in M∞,B , M∞,0 , MB,0 are sometimes called, respectively, dominant solutions, intermediate solutions, and subdominant solutions, since, ... positive solutions is particularly meaningful in the study of dominant and recessive solutions Let Advances in Difference Equations 13 R denote the set of all positive recessive solutions of 1.1 ... nonoscillatory solutions of 1.1 , we may restrict our considerations just to eventually positive solutions without loss of generality We end this section recalling the definition of recessive solution of...

Ngày tải lên: 21/06/2014, 11:20

... periodic solutions of semilinear Duffing equations, Journal of Differential Equations 105 (1993), no 2, 364–409 [5] C Fabry and D Fayyad, Periodic solutions of second order differential equations ... Periodic solutions for Li´ nard equations e Motivated by the work of [13], in this paper we use new polar coordinates [13] to investigate the existence of periodic solutions for the second- order ... periodic solutions of forced nonlinear second order ordinary differential equations, Bulletin of the London Mathematical Society 18 (1986), no 2, 173–180 [7] J.-P Gossez and P Omari, Periodic solutions...

Ngày tải lên: 22/06/2014, 22:20

... ordinary differential equations, ” in Handbook of Differential Equations: Ordinary a Differential Equations, A Canada, P Dr´ bek, and A Fonda, Eds., vol of Handbook of Differential ˇ Equations, pp 607–722, ... MSM6198959214 and by the Grant no A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic References J W Lee and D O’Regan, “Existence of solutions to some initial value, two-point, ... solvability of nonlinear singular equations subject to different types of boundary conditions In this section, we utilize Theorem 4.1 to show the existence of solutions for periodic problems The rest of...

Ngày tải lên: 21/06/2014, 20:20

... existence of a homoclinic solution for f having a linear behaviour near −∞ The proof is based on a full description of the set of all solutions of problem 1.1 , 1.10 for B < and on the existence of ... solution of problem 2.13 , 1.10 Therefore, we can borrow the arguments of 12 in the proofs of this section Theorem 3.3 If u is a damped solution of problem 1.1 , 1.10 , then u has a finite number of ... Let Me ⊂ −∞, be the set of all B such that the corresponding solutions of 1.1 , 1.10 are escape solutions The set Me is open in −∞, Proof Let B0 ∈ Me and u0 be a solution of problem 1.1 , 1.10...

Ngày tải lên: 21/06/2014, 20:20

... problem of obtaining error bounds for these asymptotic solutions to 1.2 is still open The purpose of this and the next paper Error bounds for asymptotic solutions of second- order linear difference equations ... completed the estimate of the error bounds for asymptotic solutions to second order linear difference equations in the first case For the second case, we leave it to the second part of this paper: Error ... for Asymptotic Solutions of Second- order Linear Difference Equation II: the second case In the rest of this paper, we would like to give an example to show how to use the results of this paper...

Ngày tải lên: 21/06/2014, 11:20

... behaviour of solutions of nonhomogeneous third order differential equations, ” Applicable Analysis, vol 12, no 4, pp 273–285, 1981 N Parhi, “Nonoscillation of solutions of a class of third order differential ... nonoscillation of all solutions of nonlinear functional differential equations In this connection, Parhi 10 established some sufficient conditions for oscillation of all solutions of the second- order forced ... class of nonlinear differential equations of third order, ” Bulletin ¸ of the Greek Mathematical Society, vol 39, pp 131–137, 1997 26 C Tunc and E Tunc, “On the asymptotic behavior of solutions of...

Ngày tải lên: 22/06/2014, 02:20

... Differential Equations of Parabolic Type, Prentice-Hall, New Jersey, 1964 [2] D Gilbarg and N S Trudinger, Elliptic Partial Differential Equations of Second Order, vol 224 of Fundamental Principles of Mathematical ... differential equations, ” Journal of Differential Equations, vol 23, no 1, pp 1–29, 1977 [11] J H Michael, “Barriers for uniformly elliptic equations and the exterior cone condition,” Journal of Mathematical ... elliptic equations with discontinuous coefficients,” Annali della Scuola Normale Superiore di Pisa (3), vol 17, pp 43–77, 1963 [8] D Gilbarg and J Serrin, “On isolated singularities of solutions of second...

Ngày tải lên: 22/06/2014, 22:20

... greatest solutions) , unfortunately often identified in the literature on lower and upper solutions First -order differential equations with state-dependent deviated arguments have received a lot of attention ... given lower and upper solutions The first result ensures the existence of maximal and minimal solutions, and the second one establishes the existence of the greatest and the least solutions in a particular ... prove that all solutions x of (4) obey x ≤ β on I Claim 3: The set of solutions of problem (1) in [α, β] has maximal and minimal elements The set S = {x ∈ C(I) : x is a solution of (1) , x ∈ [α,...

Ngày tải lên: 20/06/2014, 20:20

... inequalities for a class of even -order differential equations Qi-Ming Zhang∗1 and Xiaofei He2 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R China College of Mathematics ... criterion of Lyapunov Am J Math 73, 885–890 (1951) [3] Cheng, SS: Lyapunov inequalities for differential and difference equations Fasc Math 23, 25–41 (1991) [4] He, Z: Existence of two solutions of m-point ... type inequalities for second- order half-linear differential equations J Math Anal Appl 382, 792–801 (2011) 10 [12] Yang, X, Kim, Y, Lo, K: Lyapunov-type inequalities for a class of quasilinear systems...

Ngày tải lên: 20/06/2014, 21:20

... Equations on Time Scales, Birkh¨ user, Boston, Mass, a USA, 2003 M Bohner and S H Saker, “Oscillation of second order nonlinear dynamic equations on time scales,” The Rocky Mountain Journal of ... for second- order linear equations on a time scale,” Journal of Difference Equations and Applications, vol 8, no 11, pp 1061–1071, 2002 T S Hassan, “Oscillation criteria for half-linear dynamic equations ... second- order Emden-Fowler delay dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol 334, no 2, pp 847–858, 2007 13 Y Sahiner, “Oscillation of second- order...

Ngày tải lên: 21/06/2014, 05:20

... nonlinear second- order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol 296, no 1, pp 265–275, 2004 Y Sun, “Positive solutions of nonlinear second- order m-point ... 2001 21 C Bai and J Fang, “On positive solutions of boundary value problems for second- order functional differential equations on infinite intervals,” Journal of Mathematical Analysis and Applications, ... “Positive solutions of operator equations on half-line,” Journal of Mathematical Analysis and Applications, vol 314, no 2, pp 423–435, 2006 23 Y Wang, L Liu, and Y Wu, “Positive solutions of singular...

Ngày tải lên: 21/06/2014, 11:20

... to Lemma 2.3 Proof of main results Proof of Theorems 1.1 and 1.2 We only prove Theorem 1.1 since the proof of Theorem 1.2 is similar ν It is clear that any solution of (2.4) of the form (1, u) ... existence and multiplicity of nodal solutions of the nonlinear second- order two-point boundary value problems, u + f (t, u) = 0, t ∈ (0, 1), u(0) = u(1) = The proof of our main results is based ... solution of (2.2) is a pair (r, u) ∈ X, which satisfies the equation (2.2) The closure of the set nontrivial solutions of (2.2) is denoted by C, let Σ(T ) denote the set of eigenvalues of linear...

Ngày tải lên: 21/06/2014, 17:20

... which proves the first conclusion ¨ The second conclusion can be shown similarly Hence, the proof is complete Finally, we turn to the proof of Theorem 3.1 Proof of Theorem 3.1 By Propositions 3.3–3.8, ... Problems, vol of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1964 Y Shi and S Chen, “Spectral theory of second- order vector difference equations, ” Journal of Mathematical ... preliminaries including existence and numbers of eigenvalues of the coupled boundary value problems, and some properties of eigenvalues of a kind of separated boundary value problem, which will...

Ngày tải lên: 21/06/2014, 20:20

... differential equations of second order, ” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Annals of Differential ... comparison theorem of second- order differential equations see Section Remark 3.6 In the discrete case: μ t ≡ This result is the same as Sturm comparison theorem of second- order difference equations see ... differential equations of second order, ” Proceedings of the American Mathematical Society, vol 13, pp 603–610, 1962 W Leighton, “Some elementary Sturm theory,” Journal of Differential Equations, ...

Ngày tải lên: 21/06/2014, 20:20

... point of T, x = {xn }, needs not to be a solution of (1.3), we can always obtain a solution of this equation with the same tail as x We can replace the first n0 terms of x by appropriate elements of ... spaces,” Journal of Difference Equations and Applications, vol 12, no 8, pp 799–809, 2006 [9] R Medina and M I Gil’, “Delay difference equations in Banach spaces,” Journal of Difference Equations and ... Electronic e Journal of Differential Equations, vol 2004, no 22, pp 1–6, 2004 [13] M Ehrnstr¨ m, “Positive solutions for second- order nonlinear differential equations, ” Nonlinear o Analysis: Theory,...

Ngày tải lên: 22/06/2014, 19:20

... 2 Second- order differential equations The plan of this paper is as follows In Section 3, we discuss problem (1.1) for the case when r ≤ Theorem 3.1 says about extremal quasisolutions of problem ... pair (U,V ) be a coupled quasisolutions of (1.1) (U,V ) are called minimal and maximal coupled quasisolutions of (1.1) if for any else U, V coupled quasisolutions of (1.1), it holds that U(t) ... quasisolutions of problem (1.1) Now we have to prove that (y,z) are minimal and maximal coupled quasisolutions of problem (1.1) in segment [y0 ,z0 ] Let (y,z) be coupled quasisolutions of (1.1)...

Ngày tải lên: 22/06/2014, 22:20

... homogeneous second order differential equations, Journal of Differential Equations 112 (1994), no 1, 239–249 [3] M S Berger and M Schechter, On the solvability of semilinear gradient operator equations, ... subquadratic second order Hamiltonian [14] systems, Journal of Mathematical Analysis and Applications 275 (2002), no 2, 870–882 , Notes on periodic solutions of subquadratic second order systems, ... Tang, Periodic solutions of a class of non-autonomous second- order systems, Journal of Mathematical Analysis and Applications 236 (1999), no 2, 227–235 Martin Schechter: Department of Mathematics,...

Ngày tải lên: 22/06/2014, 22:20

... optimality of the obtained results Preliminaries This paper is devoted to study the stability, by using the method of lower and upper solutions, of the N-periodic solutions of the following first -order ... more precise description of the set of solutions of problem (PN ) Lemma 2.5 Assume conditions (H) and (H f ) Let u, v ∈ [α,β] be two solutions of problem (PN ) Then, one of the following statements ... set of zeros of f is the ternary Cantor set 342 Stability of periodic solutions If we look for the constant solutions of problem ∆u(n) = f u(n) , n ∈ N, (4.4) we know that they are the zeros of...

Ngày tải lên: 23/06/2014, 00:20

... ] Some results on comparison of solutions of SDE and stability of solutions of SDE were studied in [1, 4, 5] MAIN RESULTS In this paper, we provide a set control differential equation (SCDE) ... proof if we choose < δ ( ε ) ≤ ( K + 1) exp (C ) CONCLUSION In this paper we gave a new concept of set control differential equation and studied its existence of solutions A comparison of two solutions ... solution of (4.1) if only if it satisfies (4.2) on I Now, based on the theorems 3.1-3.3 of SDE we have some existence results on solutions of SCDE Firstly, we have a unique existence of solution of...

Ngày tải lên: 22/07/2014, 06:20

... nonnegative solutions for second order impulsive differential equations, ” Applied Mathematics and Computation, vol 114, no 1, pp 51–59, 2000 [17] L Chen and J Sun, “Nonlinear boundary value problem of ... ordinary differential equations, ” Nonlinear Analysis, vol 51, no 7, pp 1223–1232, 2002 [24] C Bai, “Existence of solutions for second order nonlinear functional differential equations with periodic ... differential equations, ” Journal of Mathematical Analysis and Applications, vol 318, no 2, pp 593–610, 2006 ˚ a y [20] I Rachunkov´ and M Tvrd´ , “Non-ordered lower and upper functions in second order...

Ngày tải lên: 22/06/2014, 19:20