We show, by variational methods, that there exists a set $A$ open and dense in $\{a\in L^\infty(\mathbb{R}^N)~:~ \liminf_{|x|\to\infty}a(x)\geq 0\}$ such that if $a\in A$ then the problem $ -\Delta u+u=a(x)|u|^{p-1}u$, $u\in H^1(\mathbb{R}^N)$, 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 RN
CALDIROLI, Paolo;
1998-01-01
Abstract
We show, by variational methods, that there exists a set $A$ open and dense in $\{a\in L^\infty(\mathbb{R}^N)~:~ \liminf_{|x|\to\infty}a(x)\geq 0\}$ such that if $a\in A$ then the problem $ -\Delta u+u=a(x)|u|^{p-1}u$, $u\in H^1(\mathbb{R}^N)$, with $p$ subcritical (or more general nonlinearities), admits infinitely many solutions.
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