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Existence and uniqueness results for nonlinear elliptic problems with a lower order term and measure datum. (English. Abridged French version) Zbl 1016.35026

This paper is devoted to noncoercive nonlinear problems whose prototype is \[ \begin{cases}-\Delta_p u+ b(x)|\nabla u|^\lambda= \mu\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases}\tag{1} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) \((W\geq 2)\), \(\Delta_p\) is the \(p\)-Laplacian \((1< p< N)\), \(\mu\) is a Radon measure with bounded variation on \(\Omega\), \(\lambda\geq 0\), \(b\in L^\infty(\Omega)\). Under some natural assumptions on the data of (1) the authors prove uniqueness and existence of a solution of (1).

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35J60 Nonlinear elliptic equations
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