Nonlinear nonhomogeneous singular problemsPapageorgiou, Nikolaos (Avtor)
Rǎdulescu, Vicenţiu (Avtor)
Repovš, Dušan (Avtor)
singular termsuperlinear perturbationpositive solutionnonhomogeneous differential operatornonlinear regularityminimal positive solutionsstrong comparison principleWe consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator with a growth of order ▫$(p-1)$▫ near ▫$+\infty$▫ and with a reaction which has the competing effects of a parametric singular term and a ▫$(p-1)$▫-superlinear perturbation which does not satisfy the usual Ambrosetti-Rabinowitz condition. Using variational tools, together with suitable truncation and strong comparison techniques, we prove a "bifurcation-type" theorem that describes the set of positive solutions as the parameter ▫$\lambda$▫ moves on the positive semiaxis. We also show that for every ▫$\lambda > 0$▫, the problem has a smallest positive solution ▫$u^\ast_\lambda$▫ and we demonstrate the monotonicity and continuity properties of the map ▫$\lambda \mapsto u^\ast_\lambda$▫.20202020-05-29 09:40:21Članek v reviji116612UDK: 517.956.2ISSN pri članku: 0944-2669DOI: 10.1007/s00526-019-1667-0COBISS_ID: 18823001OceCobissID: 3677529sl