Solutions to Perturbed Eigenvalue Problems of the p-Laplacian in R(N)
João Marcos do Ó · 1997
Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p\\GammaLaplacian eigenvalue problem \\Gamma\\Delta pu = f(x; u) in R N : Under the assumptions that the primitive F (x; u) of f(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\\Gammapower of u. 1 Introduction In this paper we study the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem \\Gamma\\Delta p u j \\Gamma div \\Gamma jruj p\\Gamma2 ru \\Delta = f(x; u) in R N ; (1) where u 2 D 1;p (R N ). We assume that the primitive F (x; u) of the nonlinearity f(x; u) interacts only with the first eigenvalue of some p-Laplacian eigenvalue problems with weights naturally associated with F (x; u). We also assume that f : R N \\Theta R ! R is a continuous fu...