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.