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March/April 2019 On a class of nonlinear elliptic equations with lower order terms
A. Alvino, M.F. Betta, A. Mercaldo, R. Volpicelli
Differential Integral Equations 32(3/4): 223-232 (March/April 2019).

Abstract

In this paper, we prove an existence result for weak solutions to a class of Dirichlet boundary value problems whose prototype is \begin{equation*} \label{pa} \left\{ \begin{array}{lll} -\Delta_p u =\beta |\nabla u|^{q} +c(x)|u|^{p-2}u +f & & \text{in}\ \Omega \\ u=0 & & \text{on}\ \partial \Omega , \end{array} \right. \end{equation*} where $\Omega $ is a bounded open subset of $\mathbb R^N$, $N\geq 2$, $\Delta_p u={\rm div} \left(|\nabla u|^{p-2}\nabla u\right)$, $1 < p < N$, $ p-1 < q\le p-1+\frac p N$, $\beta $ is a positive constant, $c\in L^{\frac N p}(\Omega)$ with $c\ge 0$, $c\neq 0$ and $f\in L^{(p^*)'}(\Omega).$ We further assume smallness assumptions on $c$ and $f$. Our approach is based on Schauder's fixed point theorem.

Citation

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A. Alvino. M.F. Betta. A. Mercaldo. R. Volpicelli. "On a class of nonlinear elliptic equations with lower order terms." Differential Integral Equations 32 (3/4) 223 - 232, March/April 2019.

Information

Published: March/April 2019
First available in Project Euclid: 23 January 2019

zbMATH: 07036981
MathSciNet: MR3909985

Subjects:
Primary: 35J25 , 35J60

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 3/4 • March/April 2019
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