Solvability of quasilinear elliptic equations with strong dependence on the gradient
We study the problem of existence of positive, spherically symmetric strong solutions of quasilinear elliptic equations involving -Laplacian in the ball. We allow simultaneous strong dependence of the right-hand side on both the unknown function and its gradient. The elliptic problem is studied by relating it to the corresponding singular ordinary integro-differential equation. Solvability range is obtained in the form of simple inequalities involving the coefficients describing the problem. We also study a posteriori regularity of solutions. An existence result is formulated for elliptic equations on arbitrary bounded domains in dependence of outer radius of domain.
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