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Eigenvalue type problem in $s(.,.)$-fractional Musielak-Sobolev spaces | | E. Azroul
; A. Benkirane
; M. Srati
; | | Date: |
1 Jan 2023 | | Abstract: | In this paper, first we introduce the $s(.,.)$-fractional Musielak-Sobolev
spaces $W^{s(x,y)}L_{varPhi_{x,y}}(Omega)$. Next, by means of Ekeland’s
variational principal, we show that there
exists $lambda_*>0$ such that any $lambdain(0, lambda_*)$ is an
eigenvalue for the following problem
$$label{P}
(mathcal{P}_a) left{
egin{array}{clclc}
left( -Delta
ight)^{s(x,.)}_{a_{(x,.)}} u & = & lambda |u|^{q(x)-2}u &
ext{ in }& Omega, \
u & = & 0 hspace*{0.2cm} & ext{ in } & R^Nsetminus Omega,
end{array}
ight.
$$ where $Omega$ is a bounded open subset of $R^N$ with
$C^{0,1}$-regularity and bounded boundary. | | Source: | arXiv, 2301.00467 | | Services: | Forum | Review | PDF | Favorites | |
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