## Differential and Integral Equations

### On a double resonant problem in $\Bbb R^N$

#### Abstract

It is established, via variational methods, the existence and multiplicity of solutions for a class of semilinear elliptic equations in ${{\mathbb R}^N}$. The condition on the potential implies that the associated linear problem possesses a sequence of positive eigenvalues. This fact is used to study double resonant problems under a local nonquadraticity condition at infinity and pointwise limits. For the existence of solution the nonlinearity may satisfy a critical growth condition.

#### Article information

Source
Differential Integral Equations, Volume 15, Number 11 (2002), 1335-1344.

Dates
First available in Project Euclid: 21 December 2012

Furtado, Marcelo F.; Maia, Liliane A.; Silva, Elves A. B. On a double resonant problem in $\Bbb R^N$. Differential Integral Equations 15 (2002), no. 11, 1335--1344. https://projecteuclid.org/euclid.die/1356060725