Electron. J. Diff. Equ., Vol. 2013 (2013), No. 239, pp. 1-17.

Continuous dependence of solutions for indefinite semilinear elliptic problems

Elves A. B. Silva, Maxwell L. Silva

Abstract:
We consider the superlinear elliptic problem
$$ -\Delta u + m(x)u = a(x)u^p $$
in a bounded smooth domain under Neumann boundary conditions, where $m \in L^{\sigma}(\Omega)$, $\sigma\geq N/2$ and $a\in C(\overline{\Omega})$ is a sign changing function. Assuming that the associated first eigenvalue of the operator $-\Delta + m $ is zero, we use constrained minimization methods to study the existence of a positive solution when $\widehat{m}$ is a suitable perturbation of m.

Submitted August 12, 2011. Published October 24, 2013.
Math Subject Classifications: 35J20, 35J60, 35Q55.
Key Words: Positive solution; constrained minimization; eigenvalue problem; Neumann boundary condition; unique continuation.

Show me the PDF file (312 KB), TEX file, and other files for this article.

Elves A. B. Silva
Universidade de Brasília
Departamento de Matemática
Cep 70 910 900, Brasília-DF, Brazil
email: elves@unb.br
Maxwell L. Silva
Universidade Federal de Goiás
Instituto de Matemática e Estatística
Cep 74 001 970, Goiania-GO, Brazil
email: maxwell@mat.ufg.br

Return to the EJDE web page