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Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. (Some remarks on second order quasilinear elliptic problems). (French) Zbl 0614.35034

The author considers the equation \[ (1)\quad -\Delta u+H(x,Du)+\alpha u=0\quad in\quad G \] where G is a bounded open subset of \(R^ N\), \(\alpha\geq 0\), \(H(x,p)=\lambda | p|^ m-f(x)\) for (x,p)\(\in \bar G\times R^ N\), \(m>1\), and \(f\in W^{1,\infty}(G)\) is given.
He proves some existence and uniqueness results for (1) with Neumann boundary conditions. Moreover, he studies the behaviour of solutions as \(\alpha\) tends to zero. Some results are given also for \(f\in L^ q(G)\), \(q>N.\)
It is interesting to point out that no restrictions are made on m, while similar results on quasilinear equations generally hold when \(m\leq 2\).
Reviewer: E.Mascolo

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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