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- W1977568503 abstract "We consider a number of boundary value problems involving the $p$-Laplacian. The model case is $-Delta_p u=V|u|^{p-2}u$ for $uin W_0^{1,2}(D)$ with $D$ a bounded domain in ${bf R}^n$. We derive necessary conditions for the existence of nontrivial solutions. These conditions usually involve a lower bound for a product of powers of the norm of $V$, the measure of $D$, and a sharp Sobolev constant. In most cases, these inequalities are best possible. Applications to non-linear eigenvalue problems are also discussed." @default.
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- W1977568503 date "2013-02-18" @default.
- W1977568503 modified "2023-09-27" @default.
- W1977568503 title "Existence problems for the $p$-Laplacian" @default.
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