A multiplicity result for a class of strongly indefinite asymptotically linear second order systems

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

A multiplicity result for a class of superquadratic Hamiltonian systems

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system −∆v = λf(u) in Ω, −∆u = g(v) in Ω, u = v = 0 on ∂Ω, where Ω is a smooth bounded domain in R with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz’s classical Mountain Pass Theorem, and t...

Existence of solutions for a class of second-order impulsive Hamiltonian system with indefinite linear part

We consider a class of second-order impulsive Hamiltonian system with indefinite linear part. By using saddle point theorem in critical point theory, an existence result is obtained, which extends and improves some existing results.

Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems

In this paper, we study the existence and multiplicity of periodic solutions of the following second-order Hamiltonian systems ẍ(t) + V ′(t, x(t)) = 0, where t ∈ R, x ∈ R and V ∈ C(R × R ,R). By using a symmetric mountain pass theorem, we obtain a new criterion to guarantee that second-order Hamiltonian systems has infinitely many periodic solutions. We generalize and improve recent results fro...

Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

and Applied Analysis 3 Note that the inequality (14) holds true with constantC = √ 2 if T ≥ 1/2 (see [9]). Subsequently, we may assume this condition is fulfilled. Consider a functional I : E T → R defined by