## 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.

### MSC:

 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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### References:

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