Multiple nonnegative solutions for elliptic boundary value problems involving the $p$-Laplacian
Słowa kluczowe
Variational methods, weak solutions, nonnegative solutions, p-Laplacian, Dirichlet problemAbstrakt
In this paper we present a result concerning the existence of two nonzero nonnegative solutions for the following Dirichlet problem involving the $p$-Laplacian $$ \cases -\Delta_p u=\lambda f(x,u) &\text{\rm in\ } \Omega,\\ u=0 &\text{\rm on\ } \partial \Omega, \endcases $$ using variational methods. In particular, we will determine an explicit real interval $\Lambda$ for which these solutions exist for every $\lambda\in \Lambda$. We also point out that our result improves and extends to higher dimension a recent multiplicity result for ordinary differential equations.Pobrania
Opublikowane
2005-12-01
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1.
ANELLO, Giovanni. Multiple nonnegative solutions for elliptic boundary value problems involving the $p$-Laplacian. Topological Methods in Nonlinear Analysis [online]. 1 grudzień 2005, T. 26, nr 2, s. 355–366. [udostępniono 22.7.2024].
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