Abstract
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 \(\lambda \rightarrow u_\lambda ^*\).
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Papageorgiou, N.S., Vetro, C. & Vetro, F. Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems. RACSAM 114, 45 (2020). https://doi.org/10.1007/s13398-019-00779-1
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DOI: https://doi.org/10.1007/s13398-019-00779-1
Keywords
- Nonlinear
- Nonhomogeneous differential operator
- Superlinear reaction term
- Bifurcation-type result
- Nonlinear regularity theory
- Positive solutions
- Indefinite potential