Computations Of Critical Groups Research Articles

Multiplicity of Periodic Solutions for a Higher Order Difference Equation

We study a higher order difference equation. By Lyapunov-Schmidt reduction methods and computations of critical groups, we prove that the equation has fourM-periodic solutions.

Nontrivial solutions for discrete Kirchhoff-type problems with resonance via critical groups

In this paper, we study the existence of nontrivial solutions for discrete Kirchhoff-type problems with resonance at both zero and infinity by using variational methods and the computations of critical groups.

Periodic solutions for asymptotically linear Hamiltonian system with resonance both at infinity and origin via computation of critical groups

In this paper, we study the existence of nontrivial periodic solutions for asymptotically linear Hamiltonian system which has the same linear term both at infinity and origin. By computation of critical groups at origin and infinity associated with Maslov-type index, we establish the existence for nontrivial periodic solution of the system. Moreover, some conditions employed for the computation of critical groups are weakened.

Computations of critical groups and periodic solutions for asymptotically linear Hamiltonian systems

The purpose of this paper is two-fold. Firstly, we will give some parabolic-like conditions which improve the well-known angle conditions and allow further computations of the critical groups both at degenerate critical points and at infinity. As an application, we then consider the second-order Hamiltonian systems u ″ ( t ) + ∇ H ( t , u ( t ) ) = 0 , t ∈ R , where H : R × R N → R is T-periodic in its first variable and ∇ H is asymptotically linear both at origin and at infinity. Based on the computations of the critical groups and the Morse theory, we obtain the existence and multiplicity results for periodic solutions under new classes of conditions. It turns out that our main results improve sharply some known results in the literature.

Computations of Critical Groups and Applications to Nonlinear Differential Equations With Resonance

Abstract In this paper, we develop a method to compute critical groups at degenerate critical points under more general conditions. The abstract results are used to study the existence and multiplicity of nontrivial solutions for nonlinear differential equations with resonance both at infinity and at zero.

Computations of critical groups and applications to asymptotically linear wave equation and beam equation

In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero.

Computation of critical groups in Fučı́k resonance problems

We obtain nontrivial solutions of semilinear elliptic boundary value problems with jumping nonlinearities that have resonance with respect to the Fučı́k spectrum both at zero and at infinity.

Computation of critical groups in resonance problems where the nonlinearity may not be sublinear

) under weaker assumptions that require (1.4), but not (1.7). As an applica-tion we obtain new existence results for asymptotically linear elliptic boundary valueproblems at resonance.We refer the reader to Chang [2] for a wide exposition of Morse theory. The notionofcritical groups at innity was introduced in [1].2.CriticalgroupcomputationsFirst we assume that(G

Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist

We compute critical groups in semilinear elliptic boundary-value problems in which the nonlinear term may fail to have asymptotic limits at zero and at infinity. As applications, we prove several new existence results.

Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist

We compute critical groups in semilinear elliptic boundary-value problems in which the nonlinear term may fail to have asymptotic limits at zero and at infinity. As applications, we prove several new existence results.

Computations of Critical Groups at a Degenerate Critical Point for Strongly Indefinite Functionals

Computations of Critical Groups at a Degenerate Critical Point for Strongly Indefinite Functionals

Nontrivial solutions for resonant cooperative elliptic systems via computations of critical groups

Nontrivial solutions for resonant cooperative elliptic systems via computations of critical groups

Multiple solutions results for two-point boundary value problem with resonance

In this paper we prove the existence of multiple solutions for two-point boundary value problem, which is resonant type both at origin and at infinity, and with higher eigenvalue and unbounded nonlinear terms. Our main ingredients are Morse theory and the computations of critical groups.