Strongly indefinite functionals and multiple solutions of elliptic systems

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

Perturbation from symmetry and multiplicity of solutions for strongly indefinite elliptic systems

We consider the following elliptic system:

Positive Solutions and Global Bifurcation of Strongly Coupled Elliptic Systems

In this article, we study the existence of positive solutions for the coupled elliptic system −∆u = λ(f(u, v) + h1(x)) in Ω, −∆v = λ(g(u, v) + h2(x)) in Ω, u = v = 0 on ∂Ω, under certain conditions on f, g and allowing h1, h2 to be singular. We also consider the system −∆u = λ(a(x)u+ b(x)v + f1(v) + f2(u)) in Ω, −∆v = λ(b(x)u+ c(x)v + g1(u) + g2(v)) in Ω, u = v = 0 on ∂Ω, and prove a Rabinowitz...

Critical Point Theorems concerning Strongly Indefinite Functionals and Applications to Hamiltonian Systems

Let X be a Finsler manifold. We prove some abstract results on the existence of critical points for strongly indefinite functionals f ∈ C1(X ,R) via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under a new version of Cerami-type condition instead of Palais-Smale condition. As applications, we prove the existence of multiple pe...