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Variational Approach for a Robin Problem Involving Non Standard Growth Conditions

Author

Listed:
  • Khaled Kefi

    (Faculty of Computer Sciences and Information Technology, Northern Border University, Arar 73222, Saudi Arabia
    Department of Mathematics, Faculty of Sciences, University of Tunis El Manar, Tunis 1060, Tunisia)

  • Mohammed Mosa Al-Shomrani

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this manuscript, we study a Robin problem driven by the p ( x ) -Laplacian with two parameters. − div ( | ∇ w | p ( x ) − 2 ∇ w ) = λ V ( x ) | w | q ( x ) − 2 w , x ∈ Q , | ∇ w | p ( x ) − 2 ∂ w ∂ n + θ ( x ) | w | p ( x ) − 2 = β V 1 ( x ) | w | r ( x ) − 2 w . x ∈ ∂ Q . Here, Q is a regular bounded domain in R N , λ , β > 0 , p , q are continuous functions on Q ¯ , ∂ w ∂ n is the outer unit normal derivative on ∂ Q , θ ∈ L ∞ ( ∂ Q ) , such that e s s inf x ∈ ∂ Q θ ( x ) > 0 , V is an indefinite function in L s ( x ) ( Q ) and V 1 is a non-negative one in L s 1 ( x ) ( ∂ Q ) . Using variational tools, we show the existence of a non-trivial solution.

Suggested Citation

  • Khaled Kefi & Mohammed Mosa Al-Shomrani, 2022. "Variational Approach for a Robin Problem Involving Non Standard Growth Conditions," Mathematics, MDPI, vol. 10(7), pages 1-8, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1127-:d:785121
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    References listed on IDEAS

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    1. Allaoui, Mostafa, 2018. "Robin problems involving the p(x)-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 457-468.
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