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Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n-Laplacian. (English) Zbl 0732.35028

The author studies the problem \(div(| \nabla u|^{p-2}\nabla u)=f(x,u)| u|^{p-2}\) in \(\Omega \subset {\mathbb{R}}^ n\), \(1<p\leq n\), with \(u\geq 0\) and \(u\in W_ 0^{1,p}(\Omega)\). f satisfies \(f(x,0)=0\), f(x,t)\(\geq 0\) for \(t\geq 0\) and is of critical growth.
Using variational techniques he proves an existence result.
Reviewer: R.Sperb (Zürich)

MSC:

35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
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References:

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