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Khosravi Rashti, Mahnaz, Alimohammady, ءMohsen, Ghobadi, Sirous. (1402). Multiplicity of weak solutions for the Boundary Dirichlet problem of Kirschoff type in Orlicz-Sobolev spaces. , (), -. doi: 10.30495/jnrm.2023.74085.2432
Mahnaz Khosravi Rashti; ءMohsen Alimohammady; Sirous Ghobadi. "Multiplicity of weak solutions for the Boundary Dirichlet problem of Kirschoff type in Orlicz-Sobolev spaces". , , , 1402, -. doi: 10.30495/jnrm.2023.74085.2432
Khosravi Rashti, Mahnaz, Alimohammady, ءMohsen, Ghobadi, Sirous. (1402). 'Multiplicity of weak solutions for the Boundary Dirichlet problem of Kirschoff type in Orlicz-Sobolev spaces', , (), pp. -. doi: 10.30495/jnrm.2023.74085.2432
Khosravi Rashti, Mahnaz, Alimohammady, ءMohsen, Ghobadi, Sirous. Multiplicity of weak solutions for the Boundary Dirichlet problem of Kirschoff type in Orlicz-Sobolev spaces. , 1402; (): -. doi: 10.30495/jnrm.2023.74085.2432

Multiplicity of weak solutions for the Boundary Dirichlet problem of Kirschoff type in Orlicz-Sobolev spaces

Journal of New Researches in Mathematics
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 آبان 1402  XML
نوع مقاله: research paper
شناسه دیجیتال (DOI): 10.30495/jnrm.2023.74085.2432
نویسندگان
Mahnaz Khosravi Rashti1؛ ءMohsen Alimohammady email 2؛ Sirous Ghobadi1
11- Department of Mathematics,Qaemshahr Branch,Islamic Azad University, Qaemshahr , Iran
21- Department of Mathematics,Qaemshahr Branch,Islamic Azad University, Qaemshahr , Iran 2- Department of Mathematics, Faculty of Mathematical Sciences,University of Mazandaran, Babolsar, Iran
چکیده
Abstract:



In this article, the existence of at least one and two weak solutions for the following non-linear Dirichlet boundary value problem of the Kirschoff type in Orlicz-Sobolev space, which applies to the energy function of the problem. under the Palais Smale condition, was investigated:

{█(M_0 (∫_Ω▒〖[Φ(|∇ w|)+Φ(|w|)]dx) (-div(α(|∇w|) 〗 ∇w)+ α(|w|)w)=λ_0 f_0 (x,w) in Ω,@w=0 on ∂Ω,)┤

where Ω ⊆R^N (N ≥ 3) is a bounded domain with smooth boundary ∂Ω,M_0 ∶ [0,+∞[→ R is a continuous map in which

0 < m_0 ≤ M_0 (z)≤ m_1,

for all z ≥ 0, where m0 and m1 are two suitable constants, α∶ (0,∞) → R is a map in which the induced map ϕ∶ R→R is defined by function

φ(z)={█(α(|z|)z, for z≠0,@0, for z=0,)┤



is strictly increasing homeomorphism and odd, f_0 ∶ Ω ̅×R → R as usual is an L^1-Carathéodory function and finally λ_0 > 0 is a given parameter.
کلیدواژه‌ها
Variational methods؛ elliptic problems of Kirchhoff type؛ Pelais-Small condition؛ orlicz-Sobolev space؛ critical point theory
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