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Strongly nonlinear elliptic problems near resonance: A variational approach. (English) Zbl 0715.35029

Under varying specific “resonance” or “growth” conditions, existence of a solution to the Dirichlet problem \[ -div(| \nabla u|^{p- 2}\nabla u)=f(x,u)+h(x),\quad 1<p<\infty, \] in \(\Omega \in {\mathbb{R}}^ N\), with \(u=0\) on \(\partial \Omega\), is proved. The solution minimizes the corresponding functional \[ \Phi (u)=(1/p)\int_{\Omega}| \nabla u|^ p-\int_{\Omega}F(x,u)-\int_{\Omega}h(x)u \] with \(F(x,s)=\int^{s}_{0}f(x,t)dt\).
Reviewer: R.Finn

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
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References:

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