Solutions to Perturbed Eigenvalue Problems of the p-Laplacian in R(N)

Abstract

<p>Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem</p>

<pre>-Δ_pu = ƒ(x, u) in ℝ^N.</pre>

<p>Under the assumptions that the primitive F(x, u) of ƒ(x, u) interacts only with the first eigenvalue, we look for solutions in the space D^1,p (ℝ^N). Furthermore, we assume a condition that measures how different the behavior of the function F(x, u) is from that of the p-power of u.</p>