Publication details
Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Communication in Pure and applied analysis |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.aimsciences.org/article/doi/10.3934/cpaa.2022056 |
| Doi | http://dx.doi.org/10.3934/cpaa.2022056 |
| Keywords | Singular nonlinearities; nonstandard growth; p-q Laplacian; multiplicity results; infinite positone problems; fixed point theorems |
| Description | 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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