Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 239, pp. 1-17.
Title: Continuous dependence of solutions for indefinite semilinear
elliptic problems
Authors: Elves A. B. Silva (Univ. de Brasilia, Brasilia-DF, Brazil)
Maxwell L. Silva (Univ. Federal de Goias, Goiania-GO, Brazil)
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.