A Singular ODE Related to Quasilinear Elliptic Equations
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We consider a quasilinear elliptic problem with the natural growth in the gradient. Existence, non-existence, uniqueness, and qualitative properties of positive solutions are obtained. We consider both weak and strong solutions. All results are based on the study of a suitable singular ODE of the first order. We also introduce a comparison principle for a class of nonlinear integral operators of Volterra type that enables to obtain uniqueness of weak solutions of the quasilinear equation.
CitationKorkut, L., Pasic, M., & Zubrinic, D. (2000). A singular ODE related to quasilinear elliptic equations. Electronic Journal of Differential Equations, 2000(12), pp. 1-37.
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