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 \(\lambda >0\) varies.
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Acknowledgements
The first and the second author were supported in part by the Slovenian Research Agency Grants P1-0292, J1-8131, J1-7025, N1-0064 and N1-0083. We thank the referee for comments and suggestions.
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Papageorgiou, N.S., Repovš, D.D. & Vetro, C. Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction. J Geom Anal 30, 1774–1803 (2020). https://doi.org/10.1007/s12220-019-00278-0
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DOI: https://doi.org/10.1007/s12220-019-00278-0
Keywords
- Competition phenomena
- Nonlinear regularity
- Nonlinear maximum principle
- Strong comparison principle
- Bifurcation-type result
- Almost critical growth