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1.
本文研究一类具有周期边值条件的脉冲微分方程解的存在性问题.通过运用临界点理论以及变分方法证明此系统存在周期解.  相似文献   

2.
In this paper, we study the existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses via variational methods and critical point theory. We give new sufficient conditions for the existence of subharmonic solutions with prescribed minimal period of forced pendulum equations. Our results improve some known results in the literature.  相似文献   

3.
In this paper, we study the existence of solutions for damped nonlinear impulsive differential equations with Dirichlet boundary conditions. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution. Some recent results are extended and significantly improved. Finally, some examples are presented to illustrate our main results. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

4.
姜黎鑫  丁卫 《数学杂志》2016,36(5):920-928
本文利用变分法研究了带阻尼项的脉冲系统的周期解.采用一种新的方法,在一些条件下证明了带周期边界条件的脉冲系统存在临界点.本文不仅推广了已有的结果而且还丰富了研究脉冲系统的方法.  相似文献   

5.
We study the problem of existence of conformal metrics with prescribed Q-curvature on closed four-dimensional Riemannian manifolds. This problem has a variational structure, and in the case of interest here, it is noncompact in the sense that accumulations points of some noncompact flow lines of a pseudogradient of the associated Euler–Lagrange functional, the so-called true critical points at infinity of the associated variational problem, occur. Using the characterization of the critical points at infinity of the associated variational problem which is established in [42], combined with some arguments from Morse theory, some algebraic topological methods, and some tools from dynamical system originating from Conley's isolated invariant sets and isolated blocks theory, we derive a new kind of existence results under an algebraic topological hypothesis involving the topology of the underling manifold, stable and unstable manifolds of some of the critical points at infinity of the associated Euler–Lagrange functional.  相似文献   

6.
In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.  相似文献   

7.
Recent attempts to assess the performance of SSVM algorithms for unconstrained minimization problems differ in their evaluations from earlier assessments. Nevertheless, the new experiments confirm earlier observations that, on certain types of problems, the SSVM algorithms are far superior to other variable metric methods. This paper presents a critical review of these recent assessments and discusses some current interpretations advanced to explain the behavior of SSVM methods. The paper examines the new empirical results, in light of the original self-scaling theory, and introduces a new interpretation of these methods based on anL-function model of the objective function. This interpretation sheds new light on the performance characteristics of the SSVM methods, which contributes to the understanding of their behavior and helps in characterizing classes of problems which can benefit from the self-scaling approach.The subject of this paper was presented at the ORSA/TIMS National Meeting in New York, 1978.This work was done while the author was with the Analysis Research Group, Xerox Palo Alto Research Center, Palo Alto, California.  相似文献   

8.
In this article we establish some multiplicity results for Hammerstein integral equations. The main results are based on critical point methods.  相似文献   

9.
In this paper several new multiplicity results for asymptotically linear elliptic problem at resonance are obtained via Morse theory and minimax methods. Some new observations on the critical groups of a local linking-type critical point are used to deal with the resonance case at 0.  相似文献   

10.
We start by introducing a Čech homology with compact supports which we then use in order to construct an infinite-dimensional homology theory. Next we show that under appropriate conditions on the nonlinearity there exists a ground state solution for a semilinear Schr?dinger equation with strongly indefinite linear part. To this solution there corresponds a nontrivial critical group, defined in terms of the infinite-dimensional homology mentioned above. Finally, we employ this fact in order to construct solutions of multibump type. Although our main purpose is to survey certain homological methods in critical point theory, we also include some new results. Dedicated to Felix Browder on the occasion of his 80th birthday  相似文献   

11.
In this paper, we deal with the existence and multiplicity of periodic solutions for the p(t)-Laplacian Hamiltonian system. Some new existence theorems are obtained by using the least action principle and minmax methods in critical point theory, and our results generalize and improve some existence theorems.  相似文献   

12.
We give here a general result on lower bounds for Morse indices of critical points obtained by some min-max principles. Combining this information with a semi-classical inequality yields sharp estimates on the growth of some critical values, from which we deduce new multiplicity results for solutions of semi-linear second-order elliptic equations.  相似文献   

13.
This paper deals with the critical curve of the non-Newtonian polytropic filtration equation coupled via nonlinear boundary flux. The critical global existence curve is obtained by constructing various self-similar supersolutions and subsolutions. Furthermore, we get some new results on the critical Fujita curve.  相似文献   

14.
In this paper, we are concerned with the multiplicity of solutions for a fourth-order impulsive differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and a three critical points theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. We also provide an example in order to illustrate the main abstract results of this paper.  相似文献   

15.
In this paper, we deal with the existence of periodic solutions of the p(t)-Laplacian Hamiltonian system . Some new existence theorems are obtained by using the least action principle and minimax methods in critical point theory, and our results generalize and improve some existence theorems.  相似文献   

16.
17.
In this paper, we obtain some new existence results of solutions of impulsive differential equations with periodic boundary conditions. The main tool that we use is critical point theory. Our results generalize some existing results on periodic solutions for second order ordinary differential equations even when the impulses are absent.  相似文献   

18.
Using monotonicity methods, the Lagrange multiplier rule, and some variational arguments, we consider a type of localization results pertaining to the existence of critical points to action functionals on a closed ball. A variant of the Schechter critical point theorem on a ball in Hilbert and Banach spaces is obtained. Applications to nonlinear Dirichlet problem and to partial difference equations are given in the final part of this paper.  相似文献   

19.
This paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one-dimensional solution space. We shall study the existence and multiplicity of solutions using various methods of Nonlinear Analysis such as the Lyapunov-Schmidt reduction and methods of critical point theory. The proofs are based on some general results on the oscillation and asymptotic behavior of certain parametric integrals.  相似文献   

20.
In this paper, we study the existence of multiple solutions for a class of second-order impulsive Hamiltonian systems. We give some new criteria for guaranteeing that the impulsive Hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of B. Ricceri. We extend and improve on some recent results. Finally, some examples are presented to illustrate our main results.  相似文献   

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