Existence results for a perturbed Dirichlet problem without sign condition in Orlicz spaces
UDC 517.5 We deal with the existence result for nonlinear elliptic equations related to the form$$Au + g(x, u,\nabla u) = f,$$where the term $-{\rm div}\Big(a(x,u,\nabla u)\Big)$ is a Leray–Lions operator from a subset of $W^{1}_{0}L_M(\Omega)$ into its dual.  The growth and coercivity...
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| Date: | 2020 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/373 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We deal with the existence result for nonlinear elliptic equations related to the form$$Au + g(x, u,\nabla u) = f,$$where the term $-{\rm div}\Big(a(x,u,\nabla u)\Big)$ is a Leray–Lions operator from a subset of $W^{1}_{0}L_M(\Omega)$ into its dual.  The growth and coercivity conditions on the monotone vector field $a$ are prescribed by an $N$-function $M$ which does not have to satisfy a $\Delta_2$-condition. Therefore we use Orlicz–Sobolev spaces which are not necessarily reflexive and assume that the nonlinearity $g(x,u,\nabla u)$ is a Carathéodory function satisfying only a growth condition with no sign condition. The right-hand side~$f$ belongs to $W^{-1}E_{\overline{M}}(\Omega).$ |
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| DOI: | 10.37863/umzh.v72i4.373 |