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- W2034831444 abstract "Let $Omegasubsetmathbb{R}^{N}$ be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions $a$, $b$ that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form $Lu=lambda aleft( x,tright) u^{p}-bleft( x,tright) u^{q}$ in $Omegatimesmathbb{R}$, where $0 0 $. In some cases we also show the existence of solutions $u_{lambda}$ in the interior of the positive cone and that $u_{lambda}$ can be chosen such that $lambdarightarrow u_{lambda}$ is differentiable and increasing. A uniqueness theorem is also given in the case $pleq q$. All results remain valid for the corresponding elliptic problems." @default.
- W2034831444 created "2016-06-24" @default.
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- W2034831444 date "2007-01-01" @default.
- W2034831444 modified "2023-10-03" @default.
- W2034831444 title "Periodic parabolic problems with nonlinearities indefinite in sign" @default.
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- W2034831444 doi "https://doi.org/10.5565/publmat_51107_03" @default.
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