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- W4297201744 abstract "Let $Omega subset mathbb{R}^N$, $N geq 2$, be a smooth bounded domain. We consider the boundary value problem begin{equation} label{Plambda-Abstract-ch3} tag{$P_{lambda}$} -Delta u = c_{lambda}(x) u + mu |nabla u|^2 + h(x),, quad u in H_0^1(Omega) cap L^{infty}(Omega),, end{equation} where $c_{lambda}$ and $h$ belong to $L^q(Omega)$ for some $q > N/2$, $mu$ belongs to $mathbb{R} setminus {0}$ and we write $c_{lambda}$ under the form $c_{lambda}:= lambda c_{+} - c_{-}$ with $c_{+} gneqq 0$, $c_{-} geq 0$, $c_{+} c_{-} equiv 0$ and $lambda in mathbb{R}$. Here $c_{lambda}$ and $h$ are both allowed to change sign. As a first main result we give a necessary and sufficient condition which guarantees the existence of a unique solution to eqref{Plambda-Abstract-ch3} when $lambda leq 0$. Then, assuming that $(P_0)$ has a solution, we prove existence and multiplicity results for $lambda > 0$. Our proofs rely on a suitable change of variable of type $v = F(u)$ and the combination of variational methods with lower and upper solution techniques." @default.
- W4297201744 created "2022-09-27" @default.
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- W4297201744 creator A5049845616 @default.
- W4297201744 date "2019-09-11" @default.
- W4297201744 modified "2023-09-28" @default.
- W4297201744 title "Existence and multiplicity for an elliptic problem with critical growth in the gradient and sign-changing coefficients" @default.
- W4297201744 doi "https://doi.org/10.48550/arxiv.1909.04962" @default.
- W4297201744 hasPublicationYear "2019" @default.
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