Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
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1735-4463
2008-9473
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10.61186/ijmsi
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8888
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jalali
1398
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gregorian
2019
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Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
تخصصي
Special
پژوهشي
Research paper
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<div style="color: rgb(34, 34, 34); font-family: arial, sans-serif; font-size: 12.7273px;"></div>
<p><span style="line-height: 20.8px;">The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems</span><span style="line-height: 20.8px;">$</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;">-operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;"> $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;">spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined from $W^{1}_{0}L_{M}(Omega)$ into its dual,</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;">$Phi in C^{0}(mathbb{R},mathbb{R}^{N})$. The function $g(x,u,nabla u)$ is a non linear lower</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;"> order term with natural growth with respect to $|nabla u|$, satisfying the sign condition and the</span><br style="line-height: 20.8px;" >
<span style="line-height: 20.8px;"> datum $mu$ is assumed belong to $L^1(Omega)+W^{-1}E_{overline{M}}(Omega)$.</span></p>
Elliptic equation, Orlicz-Sobolev spaces, Renormalized solution.
95
119
http://ijmsi.ir/browse.php?a_code=A-10-451-2&slc_lang=en&sid=1
M.
El Moumni
mostafaelmoumni@gmail.com
10031947532846007041
10031947532846007041
Yes
Department of Mathematics, Faculty of Sciences El Jadida, University Chouaib Doukkali