Positive solutions for nonlinear parametric singular Dirichlet problems

By Nikolaos S. Papageorgiou, Vicentiu D. Rădulescu, Dušan D. Repovš. Bulletin of Mathematical Sciences, 2018

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We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+\infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-\Delta _p,W^{1,p}_0(\Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$\lambda >0$$λ>0.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/ce07dddc57297c6c36e698997d57affe7cd44fe4

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Nonlinear nonhomogeneous singular problems (2019, result): “Previously, such bifurcation type results have been proved by Sun, Wu & Long [41], Haitao [18], Ghergu & Rădulescu [14, 15, 16] (semilinear problems driven by the Laplacian), and by Giacomoni, Schindler & Takač [17], Papageorgiou, Rădulescu & Repovš [35], Papageorgiou & Smyrlis [36], Papageorgiou, V”