Geodesic
Existence of mountain-pass solutions for p(·)-biharmonic equations with Rellich-type term
Filomat, Tome 37 (2023) no. 5, p. 1549

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This manuscript discusses the existence of nontrivial weak solution for the following nonlinear eigenvalue problem driven by the p(·)-biharmonic operator with Rellich-type term { ∆(|∆u|p(x)−2∆u) = λ |u| q(x)−2u/δ(x)2q(x) , for x ∈ Ω, u = ∆u = 0, for x ∈ ∂Ω. Considering the case 1 min x∈Ω p(x) ≤ max x∈Ω p(x) min x∈Ω q(x) ≤ max x∈Ω q(x) min { N/ 2 , Np(x)/ N −2p(x) } , we extend the corresponding result of the reference [8], for the case 1 min x∈Ω q(x) ≤ max x∈Ω q(x) min x∈Ω p(x) ≤ max x∈Ω .p(x) N 2 . The proofs of the main results are based on the mountain pass theorem.
DOI : 10.2298/FIL2305549L
Classification : 35D30, 58E05, 35J35, 47J10
Keywords: weak solutions, Navier boundary condition, Mountain Pass theorem, p(·)-Biharmonic operator, q(·)-Hardy inequality 
Mohamed Laghzal; Abdelfattah Touzani. Existence of mountain-pass solutions for p(·)-biharmonic equations with Rellich-type term. Filomat, Tome 37 (2023) no. 5, p. 1549 . doi: 10.2298/FIL2305549L
@article{10_2298_FIL2305549L,
     author = {Mohamed Laghzal and Abdelfattah Touzani},
     title = {Existence of mountain-pass solutions for p({\textperiodcentered})-biharmonic equations with {Rellich-type} term},
     journal = {Filomat},
     pages = {1549 },
     year = {2023},
     volume = {37},
     number = {5},
     doi = {10.2298/FIL2305549L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2305549L/}
}
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