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On some weakly coercive quasilinear problems with forcing
Stockholm University, Faculty of Science, Department of Mathematics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We consider the forced problem$-\Delta_p u - V(x)|u|^{p-2} u = f(x)$,where $\Delta_p$ is the $p$-Laplacian ($1<p<\infty$) in a domain $\Omega\subset \mathbb{R}^N$, $V\ge 0$ and$Q_V (u) := \int_\Omega |\nabla u|^p\, dx - \int_\Omega V|u|^p\,dx$ satisfies the condition (A) below. We show that this problem has a solution for all $f$ in a suitable space of distributions. Then we apply this result to some classes of functions $V$ which in particular include the Hardy potential \eqref{hardy2} and the potential $V(x)=\lambda_{1,p}(\Omega)$, where $\lambda_{1,p}(\Omega)$ is the Poincar\'e constant on an infinite strip.

Keyword [en]
Forced problem, Hardy potential, p-Laplacian, Poincaré constant, weakly coercive
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-146985OAI: oai:DiVA.org:su-146985DiVA: diva2:1142045
Available from: 2017-09-18 Created: 2017-09-18 Last updated: 2017-09-29Bibliographically approved

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Recent publications by Andrzej SzulkinarXiv:1709.05187

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