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This article concerns the existence and multiplicity of solutions for the singular p-biharmonic problem involving the Hardy potential and the critical Hardy-Sobolev exponent. To this end we use variational methods combined with the Mountain pass theorem and the Ekeland variational principle. We illu ...

The aim of this paper is to study existence results for a singular problem involving the ▫$p$▫-biharmonic operator and the Hardy potential. More precisely, by combining monotonicity arguments with the variational method, the existence of solutions is established. By using the Nehari manifold method, ...

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: ▫$$\begin{cases} ([u]_{s,p}^p)^{\sigma-1}(-\Delta)^s_p u = \frac{\lambda}{u^{\gamma}}+u^{ p_s^{*}-1} & \quad \text{in }\Omega,\\ u>0, & \quad \text{in }\Omega,\\ u=0, & \quad \text{in }\ma ...

In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional ▫$p$▫-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we ...