Solutions to perturbed eigenvalue problems of the p-Laplacian in R^{<small>N</small>}

• Main Author: Joao Marcos Do O
• Format: Article
• Language: English
• Published: Texas State University 1997-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Mountain Pass Theorem; Palais-Smale Condition; First eigenvalue
• Online Access: http://ejde.math.txstate.edu/Volumes/1997/11/abstr.html
• ISSN: 1072-6691

Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem $$ -Delta _pu=f(x,u)quad { m in}quad {Bbb R}^N,. $$ 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 $D^{1,p}({Bbb R}^N)$. 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 $u$.