Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 25, pp. 1-15.
Title: Existence and multiplicity results for nonlinear
elliptic problems in $R^N$ with an indefinite functional
Authors: David G. Costa (Univ. of Nevada, Las Vegas, NV, USA)
Yuxia Guo (Chinese Academy of Sciences, Beijing, China)
Miguel Ramos (Univ. de Lisboa, Lisboa, Portugal)
Abstract:
We prove the existence of a nontrivial solution for the nonlinear
elliptic problem $-\Delta u=\lambda h(x)u + a(x)g(u)$ in
$R^N$, where $g$ is superlinear near zero and near
infinity, $a(x)$ changes sign, $\lambda $ is positive, and
$h(x)\geq 0$ is a weight function. For $g$ odd, we prove the
existence of an infinite number of solutions.
Submitted June 23, 2001. Published March 4, 2002.
Math Subject Classifications: 35J25, 35J20, 58E05.
Key Words: Superlinear elliptic problems; Morse index; minimax methods.