STUDY OF SCHRÖDINGER-CHOQUARD PROBLEM WITH <i>P</i>(·)-LAPLACIAN OPERATOR

Hamza El-Houari; Elhoussain Arhrrabi; Hicham Moussa

doi:10.11948/20240146

2026 Volume 16 Issue 1

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Hamza El-Houari, Elhoussain Arhrrabi, Hicham Moussa. STUDY OF SCHRÖDINGER-CHOQUARD PROBLEM WITH P(·)-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 479-494. doi: 10.11948/20240146

Citation:

Hamza El-Houari, Elhoussain Arhrrabi, Hicham Moussa. STUDY OF SCHRÖDINGER-CHOQUARD PROBLEM WITH P(·)-LAPLACIAN OPERATOR[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 479-494. doi: 10.11948/20240146

STUDY OF SCHRÖDINGER-CHOQUARD PROBLEM WITH P(·)-LAPLACIAN OPERATOR

1.
AMNEA Group, Department of Mathematics, Faculty of Sciences and Techniques Errachidia, University Moulay Ismail, Meknes 50050, Morocco
2.
Laboratory of Systems, Control and Decision (LSCD), School of New Engineering Sciences (ENSI), Tangier 90060, Morocco
3.
Laboratory of Applied Mathematics and Scientific Computing, Faculty of Sciences and Techniques Beni Mellal, University Sultan Moulay Slimane, Morocco

Author Bio: Email: arhrrabi.elhoussain@gmail.com(E. Arhrrabi); Email: hichammoussa23@gmail.com(H. Moussa)
Corresponding author: Email: h.elhouari94@gmail.com(H. El-Houari)

Abstract

Abstract

In this paper, our focus is on a specific class of non-linear $ \psi $-Hilfer fractional generalized Schrödinger-Choquard differential equations involving the $ p(\cdot) $-Laplacian operator with Dirichlet boundary conditions. By employing the mountain pass theorem without the Palais–Smale condition, along with the Hardy-Littlewood-Sobolev inequality with variable exponents, we establish the existence of a weak solution to our problem. Our main results are novel and contribute to the literature on problems involving $ \psi $-Hilfer derivatives with the $ p(\cdot) $-Laplacian operator. This investigation enhances the scope of understanding in this specific class of problems.
- Generalized ψ-Hilfer derivative /
- Schrödinger-Choquard differential equations /
- Hardy-Littlewood-Sobolev inequality /
- mountain pass theorem
MSC: 35J60, 32C05, 35J50, 35J67, 46E35

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References

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