asymptotic solutions of nonlinear second order differential equations with variable coefficients

... Article Limit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach ˚ unkov ´ a, 1 Svatoslav Stan ek, 1 Ewa Weinm ă uller, 2 and Michael Zenz 2 1 Department of Mathematical ... the 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 ... formulate sufficient conditions for the existence of at least one solution of problem 5.1a and 5.1b with a>0. In the proof of this theorem, we work also with auxiliary two-point boundary conditions: u  0  ...

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 23/06/2014, 00:20

... structure of the set of positive solutions of parameterized nonlinear operator equations, which is essentially a consequence of Dancer 12, Theorem 2. Suppose that E is a real Banach space with norm ... P. J. Torres, “Existence of one-signed periodic solutions of some second- order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, ... pages doi:10.1155/2010/626054 Research Article Existence of Positive Solutions of Nonlinear Second- Order Periodic Boundary Value Problems Ruyun Ma, Chenghua Gao, and Ruipeng Chen Department of Mathematics, Northwest Normal...

Ngày tải lên: 21/06/2014, 11:20

... Conclusions This paper studies the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary conditions ... Difference Equations Volume 2010, Article ID 691721, 10 pages doi:10.1155/2010/691721 Research Article Existence of Solutions for Nonlinear Fractional Integro -Differential Equations with Three-Point Nonlocal ... properly cited. We prove the existence and uniqueness of solutions for nonlinear integro-differential equations of fractional order q ∈ 1, 2 with three-point nonlocal fractional boundary conditions...

Ngày tải lên: 21/06/2014, 16:20

Ngày tải lên: 22/06/2014, 19:20

... W\B r 2 (0 ) ,where B r 2 (0 ) is an open ball in W of radius r 2 centered at 0. Proof. The proof of Proposition 3.2 is the same as the proof of the condition (A2) in the proof of Theorem 3.1. We have proved the ... multiplicity of solutions for p(x)-Laplacian equations in ℝ N . Nonlinear Anal. 59, 173–188 (2004) 19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations. ... . proof of Theorem 3.1, system (1.1) has infinite solutions {u k }in W 1,p ( t ) T for ever y posi- tive integer k such that ||u k || đ +,ask đ ∞.TheproofofTheorem3.2is complete. Proof of Theorem...

Ngày tải lên: 20/06/2014, 22:20

Ngày tải lên: 22/06/2014, 11:20

Ngày tải lên: 22/06/2014, 22:20

... Article Homoclinic Solutions of Singular Nonautonomous Second- Order Differential Equations Irena Rach ˚ unkov ´ aandJanTome ˇ cek Department of Mathematical Analysis and Applications of Mathematics, Faculty of ... 1.3–1.8, 1.9 the set of solutions of 1.1, 1.10 for B ∈ L 0 , 0 consists of escape solutions and of oscillatory solutions having values in L 0 ,L and of at least one homoclinic ... 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<0 and on the existence of an escape solutions in this set. Finally,...

Ngày tải lên: 21/06/2014, 20:20

... non-linear differential equations of fractional order. Nonlinear Anal 2011, 74:792-804. 34. Zhang L, Wang G: Existence of solutions for nonlinear fractional differential equations with impulses ... W: On some nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first -order impulsive differential equations with advanced ... Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument. Nonlinear Anal 2006, 65:2013-2023. 42. Jankowski T: Positive solutions...

Ngày tải lên: 21/06/2014, 03:20

... and recessive solutions. Let Advances in Difference Equations 13 R denote the set of all positive recessive solutions of 1.1 and D denote the set of all positive dominant solutions of 1.1.FromTheorem ... Corporation Advances in Difference Equations Volume 2010, Article ID 673761, 16 pages doi:10.1155/2010/673761 Research Article Regularly Varying Solutions of Second- Order Difference Equations with Arbitrary Sign ... conditions for regular or slow variation of all positive solutions of a second- order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called M-classification...

Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 22/06/2014, 22:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... a type of the best expressive way of the structure of the solution space for recurrence relations occurring in the study of second- order linear differential equations. So, (1.3) arises with high ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS condition. Proof From the proof of Lemma 3.2, we see...

Ngày tải lên: 18/06/2014, 22:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS condition. Proof From the proof of Lemma 3.2, we see ... a type of the best expressive way of the structure of the solution space for recurrence relations occurring in the study of second- order linear differential equations. So, (1.3) arises with high...

Ngày tải lên: 20/06/2014, 04:20

... greatest solutions) , unfortunately often identified in the literature on lower and upper solutions. First -order differential equations with state-dependent deviated argu- ments have received a lot of ... a peculiar feature of equa- tions with deviated arguments, see [1] for an example with a second- order equation. Therefore, we are obliged to distinguish between the concepts of minimal solution ... (17), (18) are lower and upper solutions for problem (1) with Λ = 0, and this does not depend on the choice of τ. Proof. Reasoning in the same way as in the proof of Proposition 1, we obtain that...

Ngày tải lên: 20/06/2014, 20:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F(x) satisfies the PS condition. Proof From the proof of Lemma 3.2, we see ... properties of difference equations, those studies cover many branches of difference equations, see [3-7] and references therein. In the theory of differential equations, homoclinic solutions, ...

Ngày tải lên: 20/06/2014, 21:20

... problems for second- order difference equations. Existence of eigenvalues is proved, numbers of their eigenvalues are calculated, and their relationships between the eigenvalues of second- order difference ... studied existence of minimal and maximal quasisolutions of a second- order nonlinear periodic boundary value problem 3,Section4. In 2005, Wang and Shi 4 considered 1.1 with the periodic ... Corporation Advances in Difference Equations Volume 2009, Article ID 347291, 18 pages doi:10.1155/2009/347291 Research Article Inequalities among Eigenvalues of Second- Order Difference Equations with General Coupled...

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 22/06/2014, 22:20

... and stability in differential equations with variable delays. Nonlinear Anal. 63, e233–e242 (2005). doi:10.1016/j.na.2005.02.081 11. Sakthivel, R, Luo, J: Asymptotic stability of nonlinear impulsive ... neutral differential equations with variable delays. Proc Am Math Soc. 136, 909–918 (2008) 19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential equations with variable ... neutral differential equation, variable delays 1 Introduction The objective of this article is to investigate the stability of the zero solution of the first -order linear neutral differential equations...

Ngày tải lên: 20/06/2014, 22:20

... multiplicity of periodic solution for a class of non-autonomous second- order systems with linear nonlinearity. Nonlinear Anal. 60, 325–335 (2005) 12. Wang, Z, Zhang, J: Periodic solutions of a class of second ... follows from ( 1 ) which are appeared in the proof of Theorem 1.2. Then the proof of Theorem 1.3 is completed. □ Proof of Theorem 1.4. From the proof of Theorem 1.1, we know that  is coercive which ... of second order non-autonomous Hamiltonian systems. Nonlinear Anal. 72, 4480–4487 (2010). doi:10.1016/j.na.2010.02.023 13. Meng, Q, Tang, XH: Solutions of a second- order Hamiltonian with periodic...

Ngày tải lên: 21/06/2014, 00:20