Existence of multiple solutions for a p-Kirchhoff problem with nonlinear boundary conditions

Area of Science:

• Nonlinear Analysis
• Mathematical Physics
• Differential Equations

Background:

• Singular nonlocal elliptic problems present significant mathematical challenges.
• Understanding the existence and multiplicity of solutions is crucial for various applications.
• Previous research has explored existence but multiplicity remains an active area.

Purpose of the Study:

• To investigate the existence of multiple solutions for a specific singular nonlocal elliptic problem.
• To establish conditions guaranteeing the presence of at least two positive solutions.
• To contribute to the theory of nonlinear elliptic equations.

Main Methods:

• Application of the variational method.
• Utilizing the Nehari manifold technique.
• Analysis of a singular nonlocal elliptic problem with specific boundary conditions.

Main Results:

• The paper demonstrates the existence of at least two distinct positive solutions.
• The Nehari manifold approach successfully identifies multiple solution candidates.
• The established conditions are shown to be sufficient for guaranteeing multiple solutions.

Conclusions:

• The existence of multiple positive solutions is confirmed for the considered singular nonlocal elliptic problem.
• The variational method combined with the Nehari manifold is effective for this class of problems.
• This work advances the understanding of solution multiplicity in singular elliptic equations.