Singular perturbation problems with a compact support semilinear term

Semilinear Problems with Bounded Nonlinear Term

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.

An asymptotic numerical method for fourth order singular perturbation problems with a discontinuous source term

Singularly perturbed two-point boundary-value problems (BVPs) for fourth-order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative with a discontinuous source term is considered. The given fourth-order BVP is transformed into a system of weakly coupled systems of two second-order ODEs, one without the parameter and the other with the paramet...

On some anisotropic singular perturbation problems

We investigate the asymptotic behavior of some anisotropic diffusion problems and give some estimates on the rate of convergence of the solution toward its limit. We also relate this type of elliptic problems to problems set in cylinder becoming unbounded in some directions and show how some information on one type leads to information for the other type and conversely. 1. A model problem The g...

On Singular Perturbation Problems with Robin Boundary Condition

We consider the following singularly perturbed elliptic problem 2 u ? u + f(u) = 0; u > 0 in ; @u @ + u = 0 on @; where f satisses some growth conditions, 0 +1, and R N (N > 1) is a smooth and bounded domain. The cases = 0 (Neumann problem) and = +1 (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant > 1 such that, as ! 0, the lea...