Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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EXISTENCE OF THREE WEAK SOLUTIONS FOR A CLASS OF NONLINEAR OPERATORS INVOLVING p(x)-LAPLACIAN WITH MIXED BOUNDARY CONDITIONS

  • Aramaki, Junichi (Division of Science, Faculty of Science and Engineering Tokyo Denki University)
  • Received : 2020.12.09
  • Accepted : 2021.03.10
  • Published : 2021.09.15
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Abstract

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

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References

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