August 18, 2025Open Access

Existence of solutions for nonlinear elliptic singular inclusion problems

Key Points

Weak solutions exist for nonlinear elliptic inclusion problems with singular terms, demonstrating a key result in the analysis.
Analysis reveals that despite singularities, solutions can be obtained through approximation methods and compactness arguments.
An appropriate weak formulation framework is utilized to address difficulties arising from nonlinearities and singular terms.
This work highlights the robustness of broad assumptions on data and nonlinearity in establishing solution existence.

Abstract

In this study we investigate the existence of solutions for a particular class of nonlinear elliptic inclusion problems involving singular terms. The analysis is carried out within a weak formulation framework, and particular attention is given to the difficulties arising from the singular nature of the nonlinearities. Using appropriate approximation methods and compactness arguments, we establish the existence of weak solutions assuming broad assumptions on the given data and the nonlinearity.

Existence of solutions for nonlinear elliptic singular inclusion problems

Key Points

Abstract

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