Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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EXISTENCE AND MULTIPLICITY OF SOLUTIONS OF p(x)-TRIHARMONIC PROBLEM

  • Belakhdar, Adnane (Laboratory Nonlinear Analysis, Department of Mathematics, Faculty of Science University Mohammed 1st) ;
  • Belaouidel, Hassan (Laboratory Nonlinear Analysis, Department of Mathematics, Faculty of Science University Mohammed 1st) ;
  • Filali, Mohammed (Laboratory Nonlinear Analysis, Department of Mathematics, Faculty of Science University Mohammed 1st) ;
  • Tsouli, Najib (Laboratory Nonlinear Analysis, Department of Mathematics, Faculty of Science University Mohammed 1st)
  • Received : 2021.11.12
  • Accepted : 2022.02.23
  • Published : 2022.06.08
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Abstract

In this paper, we study the following nonlinear problem: $$\{-\Delta_{p}^{3}(x)u\;=\;{\lambda}V_{1}(x){\mid}u{\mid}^{q(x)-2}u\;in\;{\Omega},\\u\;=\;{\Delta}u\;{\Delta}^{2}u\;=\;0\;on\;{\partial}\Omega, $$ under adequate conditions on the exponent functions p, q and the weight function V1. We prove the existence and nonexistence of eigenvalues for p(x)-triharmonic problem with Navier boundary value conditions on a bounded domain in ℝN. Our technique is based on variational approaches and the theory of variable exponent Lebesgue spaces.

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