Generalized Fountain Theorem and applications to strongly indefinite semilinear problems

Compact Embeddings and Indefinite Semilinear Elliptic Problems

Our purpose is to find positive solutions u ∈ D(R ) of the semilinear elliptic problem −∆u = h(x)u for 2 < p. The function h may have an indefinite sign. Key ingredients are a h-dependent concentration-compactness Lemma and a characterization of compact embeddings of D(R ) into weighted Lebesgue spaces.

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Variational Methods for Strongly Indefinite Problems

Inevitably, reading is one of the requirements to be undergone. To improve the performance and quality, someone needs to have something new every day. It will suggest you to have more inspirations, then. However, the needs of inspirations will make you searching for some sources. Even from the other people experience, internet, and many books. Books and internet are the recommended media to hel...

Existence of a Nontrivial Solution to a Strongly Indefinite Semilinear Equation

Under general hypotheses, we prove the existence of a nontrivial solution for the equation Lu = N(u), where u belongs to a Hilbert space H , L is an invertible continuous selfadjoint operator, and N is superlinear. We are particularly interested in the case where L is strongly indefinite and N is not compact. We apply the result to the Choquard-Pekar equation -Au(x)+p(x)u(x) = u(x) f U <'y\ dy,...

Monotone Relaxation Iterates and Applications to Semilinear Singularly Perturbed Problems

This paper deals with monotone relaxation iterates for solving nonlinear monotone difference schemes of elliptic type. The monotone ω-Jacobi and SUR (Successive Under-Relaxation) methods are constructed. The monotone methods solve only linear discrete systems at each iterative step and converge monotonically to the exact solution of the nonlinear monotone difference schemes. Convergent rates of...