Arcoya, David; Martínez-Aparicio, Pedro J. Quasilinear equations with natural growth. (English) Zbl 1151.35343 Rev. Mat. Iberoam. 24, No. 2, 597-616 (2008). 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. Cited in 17 Documents MSC: 35J60 Nonlinear elliptic equations 35J65 Nonlinear boundary value problems for linear elliptic equations 35B45 A priori estimates in context of PDEs Keywords:quasilinear elliptic equations; critical growth; singular nonlinearity × Cite Format Result Cite Review PDF Full Text: DOI Euclid EuDML References: [1] Abdellaoui, B., Dall’Aglio, A. and Peral, I.: Some remarks on elliptic problems with critical growth in the gradient. J. 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Les Presses de l’Université de Montréal, Montreal, Que., 1966 · Zbl 0151.15501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.