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Zhiqing Han 《Applied mathematics and computation》2011,217(14):6516-6525
By introducing a variational framework for a class of second order nonlinear differential equations with non-separated periodic boundary value conditions, some results on the existence of non-trivial, positive and negative solutions of the problems are obtained. Some results by Atici-Guseinov, Graef-Kong, etc. obtained by topological degree methods are extended. The resonant case of the problems where the nonlinearities are unbounded and satisfy Ahmad-Lazer-Paul type conditions is also considered. 相似文献
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本文利用变分方法给出了具不对称非线性项的二阶常微分方程周期解的存在性的充分条件,通过例子说明本文的主要结果可看作是Landesman-Lazer条件的补充。 相似文献
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Shi Xia LUAN An Min MAO 《数学学报(英文版)》2005,21(4):685-690
In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems (H) ü+A(t)u+∨V(t, u)=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem. 相似文献
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Let T 1 be an integer, T = {0, 1, 2,..., T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems△u(t)- a(t)u(t) = λu(t) + f(u(t- τ(t)))- h(t), t ∈ T,u(0) = u(T),where △u(t) = u(t + 1)- u(t), a : T → R and satisfies∏T-1t=0(1 + a(t)) = 1, τ : T → Z t- τ(t) ∈ T for t ∈ T, f : R → R is continuous and satisfies Landesman-Lazer type condition and h : T → R. The proofs of our main results are based on the Rabinowitz's global bifurcation theorem and Leray-Schauder degree. 相似文献
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Periodic solutions for planar 2N-body problems 总被引:3,自引:0,他引:3
In this paper we study some necessary conditions and sufficient conditions for the nested polygonal solutions of planar 2N-body problems.
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本文研究了一类可以描述为右端不连续微分方程的循环神经网络模型.在并不要求激励函数连续、有界及单调非减的情况下,通过利用线性矩阵不等式和微分包含中的Cellina近似选择定理,得到了该神经网络模型存在周期解的充分条件.最后,给出了一个数值例子用以说明本文结果的有效性. 相似文献
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Francesca Faraci 《Journal of Mathematical Analysis and Applications》2006,319(2):567-578
This paper deals with the multiplicity of solutions of a second order nonautonomous system. We extend a previous result of the author relaxing the assumptions on the sign of the potential. 相似文献
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In this paper,using the Brouwer topological degree,the authors prove an existence result for finite variational inequalities.This approach is also used to obtain the existence of periodic solutions for a class of evolution variational inequalities. 相似文献
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高阶亚线性Duffing方程的周期解 总被引:1,自引:0,他引:1
在本文中,二阶亚线性Duffing方程周期解存在的结果被推广到高阶Duffing方:x^(2n)+g(x)=p(t)=p(t+2π)(n≥1)和x^(2n+1)+g(x)-p(t)=p(t+2π)。 相似文献
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This paper is devoted to the study of periodic solutions for a class of second-order ordinary differential equations by utilizing a technique for obtaining solutions to free problems in the calculus of variations originating in the work of Carathéodory (Ref. 1, 1935). The key of this technique is to find some suitable transformation which transfers the periodic solution problem to an equivalent variational problem in which the minimizer is more easily determined. Some applications are presented to illustrate the utility of this technique.Supported by NSFC Grant 10401013, 985 Project of Jilin University and Graduate Innovation Lab of Jilin University. The authors thank Professor D. A. Carlson and the anonymous referees for valuable suggestions and helpful comments. 相似文献
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Hao YIN 《数学年刊B辑(英文版)》2006,27(4):401-410
Abstract
This paper deals with the periodic solutions of Schr?dinger flow from S
3 to S
2. It is shown that the periodic solution is related to the variation of some functional and there exist S1-invariant critical
points to this functional. The proof makes use of the Principle of Symmetric Criticality of Palais.
*Project supported by the National Natural Science Foundation of China (No.10321001). 相似文献
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Adriana Buic? Veronica Ana Ilea 《Journal of Mathematical Analysis and Applications》2007,330(1):576-583
In this paper we study the existence of ω-periodic solutions for some functional-differential equations of mixed type. Among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities. We use here the coincidence degree theory of Mawhin. 相似文献