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Weak and Positive Solutions for Kirchhoff Type Elliptic Problems

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Abstract

By means of the Galerkin method, we prove the existence of a nontrivial weak solution for two Kirchhoff type elliptic problems under weak hypotheses on the nonlocal terms M, S and the nonlinearities f, g specified later. Moreover, for each problem, we give a regularity result for positive solutions using a bootstrap argument. Some examples are included to illustrate our results.

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Authors and Affiliations

  1. Department of Mathematics, Labo. Oper. Theo. and Part. Diff. Eq.: Foundations and Applications, University of El Oued, B.P. 789, 39000, El Oued, Algeria

    Elmehdi Zaouche

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  1. Elmehdi Zaouche
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Zaouche, E. Weak and Positive Solutions for Kirchhoff Type Elliptic Problems. Mediterr. J. Math. 18, 244 (2021). https://doi.org/10.1007/s00009-021-01902-6

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  • DOI: https://doi.org/10.1007/s00009-021-01902-6

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