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Solutions of a (p, q)-Laplacian equation involving a super-linear and a singular terms

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Abstract

In this paper, we consider the (p, q)-Laplacian problem

$$\begin{aligned} -\Delta _{p}u-\mu \Delta _{q}u+\theta (x) u^{p-1}=\beta (x) u^{p-1}+\lambda a(x) u^{-\gamma }+b(x)u^{r-1}, \end{aligned}$$

with homogeneous Dirichlet boundary condition and \(u > 0 \) in \( \Omega \), where \(\Omega \subset \mathbb {R}^N\) is an open bounded domain with smooth boundary. The existence of an interval for \(\lambda \) in which the problem has at least two positive weak solutions is proved. The main tools are Nehari manifold and the fibering method.

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  1. Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 3414896818, Iran

    A. Razani & F. Behboudi

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  1. A. Razani
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  2. F. Behboudi
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Razani, A., Behboudi, F. Solutions of a (p, q)-Laplacian equation involving a super-linear and a singular terms. Ricerche mat 72, 379–397 (2023). https://doi.org/10.1007/s11587-022-00732-2

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  • DOI: https://doi.org/10.1007/s11587-022-00732-2

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