Search results for "bifurcation-type result"
showing 3 items of 3 documents
Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction
2020
We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory 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 $$\lambda >0$$ varies.
Positive solutions for nonlinear Robin problems
2017
We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.
Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems
2020
We consider a parametric nonlinear Robin problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential. The reaction term is $$(p-1)$$-superlinear but need not satisfy the usual Ambrosetti–Rabinowitz condition. We look for positive solutions and prove a bifurcation-type result for the set of positive solutions as the parameter $$\lambda >0$$ varies. Also we prove the existence of a minimal positive solution $$u_\lambda ^*$$ and determine the monotonicity and continuity properties of the map $$\lambda \rightarrow u_\lambda ^*$$.