## 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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