Solutions of semilinear elliptic problems in shrinking annuli

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

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...

Numerical verification of positiveness for solutions to semilinear elliptic problems

In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic boundary value problems. We provide a sufficient condition for a solution to an elliptic problem to be positive in the domain of the problem, which can be checked numerically without requiring a complicated computation. Although we focus on the homogeneous Dirichlet case in this paper...

Existence of Solutions for Semilinear Elliptic Problems without (ps) Condition

We establish an existence result for semilinear elliptic problems with the associated functional not satisfying the Palais-Smale condition. The nonlinearity of our problem does not satisfy the Ambrosetti-Rabinowitz condition.

Multiple Clustered Layer Solutions for Semilinear Elliptic Problems on S

We consider the following superlinear elliptic equation on Sn  ε∆Snu− u+ f(u) = 0 in D; u > 0 in D and u = 0 on ∂D, where D is a geodesic ball on Sn with geodesic radius θ1, and ∆Sn is the Laplace-Beltrami operator on Sn. We prove that for any θ ∈ ( 2 , π) and for any positive integer N ≥ 1, there exist at least 2N + 1 solutions to the above problem for ε sufficiently small. Moreover, the asym...