Perturbed nonlinear degenerate problems in $\mathbb R^N $
Volume 36 / 2009
Applicationes Mathematicae 36 (2009), 213-223
MSC: 35J60, 35J65, 35J70.
DOI: 10.4064/am36-2-8
Abstract
Via critical point theory we establish the existence and regularity of solutions for the quasilinear elliptic problem $$ \left\{\eqalign{ &{-}\textrm{div} \mathcal{A}(x, \nabla u) + a(x)\vert u \vert^{p-2} u = g(x)|u|^{p-2}u + h(x)|u|^{s-1}u \quad\ \hbox{in } {\Bbb R}^N,\cr &u>0,\quad\ \lim_{\vert x \vert \rightarrow \infty} u(x) = 0,}\right. $$ where $ 1< p< N $; $ a(x) $ is assumed to satisfy a coercivity condition; $ h(x)$ and $ g(x)$ are not necessarily bounded but satisfy some integrability restrictions.
