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

作者：Marcelo Fernandes Furtado, Liliane A. Maia, Elves A. B. Silva · 发表于：Differential and Integral Equations · 年份：2002 · DOI：10.57262/die/1356060725 · 被引用次数：19 · 研究领域：Spectral Theory in Mathematical Physics、Numerical methods in inverse problems、Differential Equations and Boundary Problems

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.