Differential and Integral Equations

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

Marcelo F. Furtado, Liliane A. Maia, and Elves A. B. Silva

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060725

Mathematical Reviews number (MathSciNet)
MR1920690

Zentralblatt MATH identifier
1034.35024

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B33: Critical exponents 35J20: Variational methods for second-order elliptic equations

Citation

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


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