Positive bounded solutions for semilinear elliptic equations in smooth domains

Multiple Solutions for Singularly Perturbed Semilinear Elliptic Equations in Bounded Domains

We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains Ω:−ε2∆u+ a(·)u= u|u|p−2 in Ω, u > 0 in Ω, u= 0 on ∂Ω. The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile of a(·) from the variational point of view. It is shown that if a has a “peak” in Ω, the...

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Minimal positive solutions for systems of semilinear elliptic equations

The paper is devoted to a system of semilinear PDEs containing gradient terms. Applying the approach based on Sattinger’s iteration procedure we use sub and supersolutions methods to prove the existence of positive solutions with minimal growth. These results can be applied for both sublinear and superlinear problems.

Symmetry-Breaking for Positive Solutions of Semilinear Elliptic Equations

In a recent interesting paper, GIDAS, NI, and NIRENBERG [2] proved that positive solutions of the Dirichlet problem for second-order semi-linear elliptic equations on balls must themselves be spherically symmetric functions. Here we consider the bifurcation problem for such solutions. Specifically, we investigate the ways in which the symmetric solution can bifurcate into a nonsymmetric solutio...

Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

Correspondence should be addressed to Faten Toumi, [email protected] Received 18 June 2010; Accepted 25 September 2010 Academic Editor: A. Mikelic Copyright q 2010 Faten Toumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Thi...