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Existence of positive solutions to nonlinear elliptic problem in NTA-conical domains. (English) Zbl 1321.35014

Summary: We study the existence and the asymptotic behavior of positive solutions of the nonlinear equation \[ \Delta u+ \phi(.,u)+\psi(.,u)=0, \] in NTA-cones in \(\mathbb{R}^n (n\geq 3)\).

MSC:

35J08 Green’s functions for elliptic equations
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
31B35 Connections of harmonic functions with differential equations in higher dimensions
35B09 Positive solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
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Full Text: Euclid