In this paper, we proved the existence and the multiplicity of solutions for some $ p(x) $-biharmonic problems involving singular nonlinearity and a Hardy potential. More precisely, by the use of the min-max method, we proved the existence of a nontrivial solution for such a problem. Next, diversions of the mountain pass theorem were used to prove the multiplicity of solutions.
Citation: Abdeljabbar Ghanmi, Abdelhakim Sahbani. Existence results for $ p(x) $-biharmonic problems involving a singular and a Hardy type nonlinearities[J]. AIMS Mathematics, 2023, 8(12): 29892-29909. doi: 10.3934/math.20231528
In this paper, we proved the existence and the multiplicity of solutions for some $ p(x) $-biharmonic problems involving singular nonlinearity and a Hardy potential. More precisely, by the use of the min-max method, we proved the existence of a nontrivial solution for such a problem. Next, diversions of the mountain pass theorem were used to prove the multiplicity of solutions.
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Abdeljabbar Ghanmi, Abdelhakim Sahbani. Existence results for $ p(x) $-biharmonic problems involving a singular and a Hardy type nonlinearities[J]. AIMS Mathematics, 2023, 8(12): 29892-29909. doi: 10.3934/math.20231528
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