Some new weighted compact embeddings results and existence of weak\n solutions for eigenvalue Robin problem

2020/11/21 by İsmail Aydın, Aydin, Ismail, Cihan Ünal +2
Computer Science · Mathematics · #35J70 #46E35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J35 #Secondary 35J60

paper · pdf · doi:10.48550/arxiv.2011.10847

openalex publication_date 2020/11/21 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational\nprinciple, Fountain Theorem, we prove the existence and multiplicity of\nsolutions for the following Robin problem \
left
\n\-
textdiv
left( a(x)
left
vert
nabla u
right
vert\n^p(x)-2
nabla u
right) =
lambda b(x)
left
vert u
right
vert ^q(x)-2u, · amp;\nx
in
Omega

a(x)
left
vert
nabla u
right
vert ^p(x)-2
frac
partialν
partial
upsilon +
beta (x)
left
vert u
right
vert ^p(x)-2u=0, · amp; x
in\n
partial
Omega , \
right. under some appropriate\nconditions in the space W_a,b^1,p(.)\( \Ω \).\n

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