MULTIPLE POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC EQUATIONS IN ESTEBAN-LIONS DOMAINS WITH HOLES

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Multiple Nontrivial Solutions of Elliptic Semilinear Equations

We find multiple solutions for semilinear boundary value problems when the corresponding functional exhibits local splitting at zero.

Multiple Positive Solutions for a Class of Concave-Convex Semilinear Elliptic Equations in Unbounded Domains with Sign-Changing Weights

Correspondence should be addressed to Tsing-San Hsu, [email protected] Received 8 September 2010; Accepted 18 October 2010 Academic Editor: Julio Rossi Copyright q 2010 Tsing-San Hsu. 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 c...

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...