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arXiv · 1905.10609

Singular elliptic problems with unbalanced growth and critical exponent

Deepak Kumar·V. D. Radulescu·K. Sreenadh
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Abstract

In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -Δ_{p}u-\baΔ_{q}u & = \la u^{-\de}+ u^{r-1}, \ u>0, \ \text{ in } \Om \\ u&=0 \quad \text{ on } \pa\Om, \end{array} \right. \end{equation*} where $\Om$ is a bounded domain in $\mathbb{R}^n$ with smooth boundary, $1< q< p p$ and $\la,\, \ba>0$ are parameters. We prove existence, multiplicity and regularity of weak solutions of $(P_\la)$ for suitable range of $\la$. We also prove the global existence result for problem $(P_\la)$.

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Deepak Kumar, V. D. Radulescu, K. Sreenadh. 2020-03-17. Singular elliptic problems with unbalanced growth and critical exponent. https://doi.org/10.1088/1361-6544%2Fab81ed

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