Multiple nonnegative solutions for elliptic boundary value problems involving the $p$-Laplacian
Keywords
Variational methods, weak solutions, nonnegative solutions, p-Laplacian, Dirichlet problemAbstract
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.Downloads
Published
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 December 2005. Vol. 26, no. 2, pp. 355 - 366. [Accessed 18 February 2025].
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