Differential Systems with Strongly Indefinite Variational Structure

Diierential Systems with Strongly Indeenite Variational Structure

We study the existence of non-trivial solutions for a class of problems containing in particular the following system of two coupled semilinear Poisson equations: (I) 8 > < > : ? v = f(u) in ; ? u = g(v) in ; u = v = 0 on @: (1) (2) (3) Here is a bounded domain in R N with a smooth boundary, and is the Laplace operator. Problem (I) allows for a variational formulation, i.e. solutions arise as c...

Variational Methods for Strongly Indefinite Problems

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On a superquadratic elliptic system with strongly indefinite structure

In this paper, we consider the elliptic system

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...

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems