Positive solutions for nonlinear Robin problems
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, existenc...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/204/abstr.html |
| Summary: | 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 $\lambda\to \tilde{u}_\lambda$. |
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| ISSN: | 1072-6691 |