Anisotropic equations with indefinite potential and competing nonlinearitiesPapageorgiou, Nikolaos (Avtor)
Rǎdulescu, Vicenţiu (Avtor)
Repovš, Dušan (Avtor)
variable exponent spacesregularity theorymaximum principleconcave and convex nonlinearitiespositive solutionscomparison principlesWe consider a nonlinear Dirichlet problem driven by a variable exponent ▫$p$▫-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and a convex (superlinear) perturbation (the anisotropic concave-convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter ▫$\lambda$▫ varies. Also, we prove the existence of minimal positive solutions.20202020-09-14 10:21:27Članek v reviji119968sl