What question did this study set out to answer?

The aim is to investigate the singular Dirichlet problem driven by a variable growth differential operator and determine the unique bounded solution.

July 12, 2026Open Access

Singular elliptic equations with (p(z), q(z))-growth

WMWitold MajdakAGH University of Krakow NPNikolaos S. PapageorgiouNational Technical University of Athens

Key Points

The aim is to investigate the singular Dirichlet problem driven by a variable growth differential operator and determine the unique bounded solution.
Utilized approximations to analyze the singular problem.
Focused on a variable unbalanced growth differential operator.
Considered singular reactions with unbounded coefficients.
Demonstrated the existence of a unique bounded solution to the problem.
Showed the influence of the variable coefficient and exponent on the solution.
Concluded that the solution is valid near the boundary of the domain.

Abstract

Abstract We consider a singular Dirichlet problem driven by a variable unbalanced growth differential operator and a singular reaction with an unbounded coefficient and an exponent C () η ∈ C (Ω ¯) which is less than 1 only near ∂ Ω. Using approximations, we show that the problem has a unique bounded solution.

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