Singular p-Laplacian equations with superlinear perturbation

By Nikolaos S. Papageorgiou, Patrick Winkert. Journal of Differential Equations, 2019

60 citations recorded by the source corpus.

Abstract We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ > 0 varies. In addition, we show that for every admissible parameter λ > 0 the problem has a smallest positive solution u ‾ λ and we establish the monotonicity and continuity properties of the map λ → u ‾ λ .

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/cf06c135ebd41951c0c5daf1e3a23bf4e003dc22

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Nonlinear nonhomogeneous singular problems (2019, background): “placian), and by Giacomoni, Schindler & Takaˇc [17], Papageorgiou, Ra˘dulescu & Repovˇs [35], Papageorgiou & Smyrlis [36], Papageorgiou, Vetro & Vetro [37], Papageorgiou & Winkert [38] (nonlinear problems driven by the p-Laplacian). In all these works the singular term has the sp”
An existence result for singular Finsler double phase problems (2020, methodology): “On the other hand, by the Brezis-Lieb lemma, see, for example, Papageorgiou-Winkert [38, Lemma 4.1.22], we have lim inf n→∞ ⎛ ⎝∫ |un|p∗ dx − ∫ |u|p∗ dx ⎞ ⎠= lim inf n→∞ ∫ |un − u|p∗ dx.”