Nonlinear singular problems with gradient dependence

Han, Jiangfeng

doi:10.1007/s41478-025-01021-5

Nonlinear singular problems with gradient dependence

2026-01-01

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Papageorgiou, Nikolaos S.

DOI：10.1007/s41478-025-01021-5

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Abstract

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We consider a Dirichlet problem driven by a nonlinear nonhomogeneous differential operator, with a reaction which exhibits the combined effects of a parametric singular term and of a Carath & eacute;odory gradient dependent perturbation. Using the theory of nonlinear operators of monotone type, we show that for all small values of the parameter the problem has at least one positive smooth solution.

Keywords:

Nonhomogeneous differential operator

Truncation

Operator of monotone type

Nonlinear regularity theory

Nonlinear maximum principle

Singular term

Nonlinear singular problems with gradient dependence

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