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Parameter dependence for the positive solutions of nonlinear, nonhomogeneous Robin problems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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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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Acknowledgements

The authors wish to thank a knowledgeable referee for his/her remarks and constructive criticism.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy

    Calogero Vetro

  3. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Francesca Vetro

  4. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Francesca Vetro

Authors
  1. Nikolaos S. Papageorgiou
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  2. Calogero Vetro
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  3. Francesca Vetro
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Correspondence to Francesca Vetro.

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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

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