Quasilinear equations with natural growth. (English) Zbl 1151.35343

Summary: We study the existence of positive solution \(w\in H_0^1(\Omega)\) of the quasilinear equation \(-\Delta w+ g(w)|\nabla w|^2=a(x)\), \(x\in \Omega\), where \(\Omega\) is a bounded domain in \(\mathbb R^N\), \(0\leq a\in L^\infty (\Omega )\) and \(g\) is a nonnegative continuous function on \((0,+\infty)\) which may have a singularity at zero.


35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35B45 A priori estimates in context of PDEs
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