We show, by variational methods, that there exists a set $\AA$ open and dense in $\{ a\in L^\infty(\R^N):\liminf_{|x|\to\infty}a(x)\geq 0\}$ such that if $a\in \AA$ then the problem $ -\Delta u+u=a(x)|u|^{p-1}u$, $u\in H^1(\R^N)$, with $p$ subcritical (or more general nonlinearities), admits infinitely many solutions.
Genericity of the existence of infinitely many solutions for a class of semilinear elliptic equations in R^N
ALESSIO, FRANCESCA GEMMA;MONTECCHIARI, Piero
1998-01-01
Abstract
We show, by variational methods, that there exists a set $\AA$ open and dense in $\{ a\in L^\infty(\R^N):\liminf_{|x|\to\infty}a(x)\geq 0\}$ such that if $a\in \AA$ then the problem $ -\Delta u+u=a(x)|u|^{p-1}u$, $u\in H^1(\R^N)$, with $p$ subcritical (or more general nonlinearities), admits infinitely many solutions.File in questo prodotto:
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