On the existence of positive solutions for semilinear elliptic equations with singular lower order coefficients and Dirichlet boundary conditions
The authors give sufficient conditions which guarantee the existence of at least one positive solution to the Dirichlet problem for the semilinear elliptic equation in \(D\subset\mathbb{R}^n\), \(n\geq 3\), where \(D\) satisfies an exterior cone condition. The principal part of this equation is the Laplacian, and the minor terms are singular in the Kato class, which is, roughly speaking, \(L^p(\mathbb{R}^n)\) for \(p>{n\over 2}\). This type of equations is used to model steady-state diffusion-convection-reaction processes. An appropriate linear elliptic problem is considered that by means of implicit probabilistic representation supplies necessary a priori estimates which are exploited to apply the Schauder fixed point theorem.
scientific article; zbMATH DE number 1395783