Masarykova univerzita

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Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

Autoři 2022 Článek v odborném periodiku Communication in Pure and applied analysis https://www.aimsciences.org/article/doi/10.3934/cpaa.2022056 http://dx.doi.org/10.3934/cpaa.2022056 Singular nonlinearities; nonstandard growth; p-q Laplacian; multiplicity results; infinite positone problems; fixed point theorems This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of $p$-$q$ type and singular nonlinearities\left\{ \begin{alignedat}{2} {} - \mathcal{L}_{p,q} u & {} = \lambda \frac{f(u)}{u^\gamma}, \ u>0 && \quad\mbox{ in } \, \Omega, \\ u & {} = 0 && \quad\mbox{ on } \partial\Omega, \end{alignedat} \right.where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with $C^2$ boundary, $N \geq 1$, $\lambda >0$ is a real parameter,$\mathcal{L}_{p,q} u : = {\rm{div}}(|\nabla u|^{p-2} \nabla u + |\nabla u|^{q-2} \nabla u),$\$ 1

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