the method of model solutions for equations on the entire axis

... cannot be used to construct the subsolution of p x -Laplacian problems, even if the first eigenfunction of p x -Laplacian exists .On the existence of solutions for p x Laplacian equations Dirichlet ... are rare There are many papers on the existence of solutions for p-Laplacian boundary value problems via subsuper solution method see 20–24 But results on the sub-super-solution method for p x ... Proof of Theorem 1.1 From Lemmas 2.5 and 2.6, we only need to prove the existence of solutions for SBVP with 1.1 Obviously, u is a solution of SBVP with 1.1 if and only if u is a solution of...

Ngày tải lên: 22/06/2014, 03:20

Ngày tải lên: 14/03/2014, 13:20

... akroutkamel@gmail.com; ∗ Corresponding author Abstract In this paper, we are interested on the study of the nonexistence of nontrivial solutions for the p (x) −Laplacian equations, in unbounded domains of Rn This ... (x) F (u) ≥ , ∀x ∈ ∂Ω Therefore, the problem admits only the null solution Proof Similar to the proof of theorem 1,pk (x) theorem 3.3 If uk ∈ W0 (Ω) ∩ L∞ Ω solution of the system (1.6) − (1.7), ... in the study of the nonexistence of nontrivial solutions for the p (x)-laplacian problem −∆p(x) u = H (x) f (u) in Ω Bu = on ∂Ω (1.1) with u Bu = Dirichlet condition Neumann condition ∂u ∂ν (1.2)...

Ngày tải lên: 20/06/2014, 21:20

... Under the superlinear conditions 1.5 , there is no twist condition for f, which brings difficulty to the study of the existence of periodic solutions of 1.4 But we can use minimax methods to consider ... periodic solutions of the equations is obtained The previous papers concern mainly autonomous differential delay equations In this paper, we use minimax methods directly to study the following nonautonomous ... Proceedings of the National Academy of Sciences of the United States of America, vol 40, no 4, pp 708–713, 1954 T Furumochi, “Existence of periodic solutions of one-dimensional differential-delay equations, ”...

Ngày tải lên: 21/06/2014, 20:20

... i They established a corresponding iterative scheme for the problem by using the monotone iterative technique All the above works were done under the assumption that the nonlinear term is nonnegative ... difficult to find positive solutions of the pLaplacian equation when the nonlinearity changes sign In particular, little work has been done on the existence of positive solutions for higher order p-Laplacian ... nonnegative The key conditions used in the above papers ensure that positive solution is concave down If the nonlinearity is negative somewhere, then the solution needs no longer to be concave down...

Ngày tải lên: 21/06/2014, 20:20

... best of our knowledge, few papers have been published on the existence of solutions for second-order boundary value problem of impulsive dynamic equations on time scales via critical point theory ... Z Zhou, “Existence of weak solutions of two-point boundary value problems for secondorder dynamic equations on time scales,” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 4, ... Difference Equations Remark 4.1 H3 is the well-known Ambrosetti-Rabinowitz condition from the paper 27 Lemma 4.2 Suppose that the conditions (H1)–(H4) are satisfied, then ϕ satisfies the Palais-Smale condition...

Ngày tải lên: 21/06/2014, 20:20

... periodic solutions for such equations, which generalize many known results for differential equations when the time scales are chosen as the set of the real numbers The main method is based on the ... properties of the exponential function on time scales and obtain a sufficient and necessary condition that a t x t h t guarantees the existence of the periodic solutions of the equation xΔ t In ... solutions of this class of nonautonomous scalar dynamic equations on time scales, the approach that authors used in this paper is based on Mawhin’s continuation theorem In this paper, we consider the...

Ngày tải lên: 21/06/2014, 20:20

... in the proof of the uniqueness of strong solutions Global existence of strong solutions In this section, we prove the global existence of strong solutions to the problem 1.2 – 1.7 by applying the ... uniqueness of solutions of the Navier-Stokes equations for isentropic compressible fluids In fact, one also can show the global existence of weak solutions without uniqueness if the compatibility conditions ... completes the proof of Theorem 1.1 except the uniqueness assertion because of the presence of vacuum , which will be proved in the next section Uniqueness and stability of strong solutions In this...

Ngày tải lên: 22/06/2014, 06:20

... show the existence of approximate solutions of the auxiliary problems for the equilibrium problem, and establish the strong convergence of the approximate solutions to an exact solution of the ... definitions of convexity and strong convexity, respectively Remark 2.3 h is strongly monotone with the constant σ > if h is strongly convex with a constant σ/2 In fact, by the strong convexity of ... (ii) of Theorem 3.2 holds (d) Assumption (iii) of Theorem 3.2 can be obtained by Lemmas 2.12 and 2.13, and conditions (i) and (iii) (see [2]) Thus, the conclusions of the theorem follows from the...

Ngày tải lên: 22/06/2014, 18:20

... in the proof of the uniqueness of strong solutions Global existence of strong solutions In this section, we prove the global existence of strong solutions to the problem 1.2 – 1.7 by applying the ... uniqueness of solutions of the Navier-Stokes equations for isentropic compressible fluids In fact, one also can show the global existence of weak solutions without uniqueness if the compatibility conditions ... completes the proof of Theorem 1.1 except the uniqueness assertion because of the presence of vacuum , which will be proved in the next section Uniqueness and stability of strong solutions In this...

Ngày tải lên: 22/06/2014, 19:20

... exploration in mathematics Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete mathematics Further, the study of time scales ... be seen as a generalization of that in ordinary differential equations Recently, the existence and multiplicity of positive solutions for nonlinear differential equations on time scales have been ... short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform cross section and composed of N parts of different densities can...

Ngày tải lên: 20/06/2014, 20:20

... get the last inequality in (2.9) and (2.10) Thus, we have completed the proof of Lemma 2.5 □ Proof of main results Proof of Theorem 1.1 Adding the inner product of u with the first equation of ... regularity criteria for the 3D viscous MHD equations Forum Math (2010, in press) 35 Beale, J, Kato, T, Majda, A: Remarks on the breakdown of smooth solutions for the 3D Euler equations Commun Math ... regularity for solutions of micropolar fluid equations J Math Anal Appl 351, 340–349 (2009) doi:10.1016/j.jmaa.2008.10.026 19 Ortega-Torres, E, Rojas-Medar, M: On the regularity for solutions of the...

Ngày tải lên: 21/06/2014, 01:20

... and they give rise to many applications see Not only the new theory of the so-called “dynamic equations unifies the theories of differential equations and difference equations but also extends these ... concerning the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to 5–18 Recently, Erbe et al 19–21 considered the asymptotic behavior of ... Difference Equations ≤ i ≤ n − are nonnegative functions on t1 , ∞ where pi t T and lim eq t, t1 < ∞, 2.12 t→∞ with q t conditions: n−1 i t ≥ t1 , then every solution x of 1.1 satisfies one of the following...

Ngày tải lên: 21/06/2014, 05:20

... In the proof of Theorem 1.1, the condition that F2 n, x ≥ for n, x ∈ J × R, |x| ≤ in F1 , is only used in the the proofs of assumption ii of Lemma 2.1 Therefore, we only proves assumption ii of ... authors studied the existence of periodic solutions, subharmonic solutions, and homoclinic solutions of some special forms of 1.1 by using the critical point theory These papers show that the critical ... point method is an effective approach to the study of periodic solutions for difference equations Along this direction, Ma and Guo 13 applied the critical point theory to prove the existence of homoclinic...

Ngày tải lên: 21/06/2014, 11:20

... inequalities, we obtain sufficient conditions for the existence of periodic solutions for 1.3 The Lyapunov stability of periodic solutions for the equation will then be established Finally, an example ... least one nonconstant T -periodic solution if one of the following conditions holds: p > 2, p and 1/|1 − |c|| α1 T α2 T/π l−1 Proof Let Ω1 be defined as in Theorem 3.1 If y t the proof of Theorem ... periodic solutions for neutral functional differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol 54, no 7, pp 1285–1306, 2003 S Lu, “Existence of periodic solutions for a...

Ngày tải lên: 21/06/2014, 16:20

... exploration in mathematics Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete mathematics Further, the study of time scales ... be seen as a generalization of that in ordinary differential equations Recently, the existence and multiplicity of positive solutions for nonlinear differential equations on time scales have been ... short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform cross section and composed of N parts of different densities can...

Ngày tải lên: 21/06/2014, 17:20

... exploration in mathematics Motivating the subject is the notion that dynamic equations on time scales can build bridges between continuous and discrete mathematics Further, the study of time scales ... be seen as a generalization of that in ordinary differential equations Recently, the existence and multiplicity of positive solutions for nonlinear differential equations on time scales have been ... short) arise in a variety of different areas of applied mathematics and physics For example, the vibrations of a guy wire of a uniform cross section and composed of N parts of different densities can...

Ngày tải lên: 21/06/2014, 17:20

... that they involve the nonlocal coefficient M (t) To prove Theorems 1.1–1.3, we use the results of [37] on the global C 1,α regularity of the weak solutions for the p(x)-Laplacian equations The main ... extended the Brezis– Nirenberg type theorem to the case of the p(x)-Kirchhoff [50, Theorem 1.1] The Theorem 1.1 of [50] concerns with the Dirichlet problems, but the method for proving the theorem ... refer the reader to [7–11] for an overview of and references on this subject, and to [12–16] for the study of the variable exponent equations and the corresponding variational problems f The problem...

Ngày tải lên: 21/06/2014, 17:20

... Difference Equations It is obvious that under these two conditions, ϕ is an homeomorphism from R onto R and is increasing on R Recall that p-Laplacian equations have been of great interest for many mathematicians ... than ϕp in 1.3 Since there is no concrete form for the p-Laplacian-like operator ϕ of 1.1 , it is more difficult to prove the existence of periodic solutions to 1.1 Therefore, in this paper, we ... suggestions and comments, which improved the quality of this paper The work was supported by the NSF of China, the NSF of Jiangxi Province of China 2008GQS0057 , the Youth Foundation of Jiangxi...

Ngày tải lên: 21/06/2014, 18:20

... KM x for some positive constants Km , KM They established the existence results for at least one positive solution by using a fixed point theorem of cone expansion and compression of functional ... fixed-point theorem for operators on a cone, they obtained some existence of at least three positive solutions for the above problem However, to the best of our knowledge, there has not any results concerning ... least one ∞, similar to the second part of Theorem 3.1, we have Au ≥ u for Proof Since f0 u ∈ P ∩ ∂ΩH3 By f∞ ∈ 0, ϕp A1 , similar to the second part of proof of Theorem 3.4, we have Au ≤ u for...

Ngày tải lên: 21/06/2014, 20:20