We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Carathéodory terms. One is parametric, (p-1)-sublinear with a partially concave nonlinearity near zero. The other is (p- 1) -superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter λ> 0 varies.
Papageorgiou N.S., Repovs D.D., Vetro C. (2020). Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction. THE JOURNAL OF GEOMETRIC ANALYSIS, 30(2), 1774-1803 [10.1007/s12220-019-00278-0].
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
Vetro C.
2020-01-01
Abstract
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Carathéodory terms. One is parametric, (p-1)-sublinear with a partially concave nonlinearity near zero. The other is (p- 1) -superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter λ> 0 varies.
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