Multiple solutions for equations involving bilinear, coercive and compact forms with applications to differential equations

TL;DR

This paper investigates the existence of multiple fixed points for certain bilinear, coercive, and compact forms in Banach spaces, with applications to integral equations from boundary value problems in differential equations.

Contribution

It establishes conditions for multiple solutions in fixed point problems involving bilinear and coercive forms, extending to applications in differential equation boundary value problems.

Findings

Multiple fixed points exist under specified conditions.

Applications to integral equations from boundary value problems.

Provides theoretical framework for solution multiplicity.

Abstract

The existence of multiple fixed points for the coercive, bilinear, compact forms defined in the cone in the Banach space. Multiple applications to the integral equations derived from BVPs for differential equations are provided.