Abstract
In this paper we present a result concerning the existence of two nonzero nonnegative solutions for the following Dirichlet problem involving the $p$-Laplacian $$ \begin{cases} -\Delta_p u=\lambda f(x,u) &\text{\rm in\ } \Omega,\\ u=0 &\text{\rm on\ } \partial \Omega, \end{cases} $$ 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.
Citation
Giovanni Anello. "Multiple nonnegative solutions for elliptic boundary value problems involving the $p$-Laplacian." Topol. Methods Nonlinear Anal. 26 (2) 355 - 366, 2005.
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