What question did this study set out to answer?

This study aims to find infinitely many weak solutions to a specific nonlinear Kirchhoff equation with sublinear nonlinearities.

June 12, 2026

Kirchhoff Equation with New Local Sublinear Nonlinearities

Key Points

This study aims to find infinitely many weak solutions to a specific nonlinear Kirchhoff equation with sublinear nonlinearities.
Applied variational methods and a symmetric version of the mountain pass theorem.
Examined an equation involving potential V(x) and studied its sublinear characteristics.
Provided several examples demonstrating the application of the main results.
Established the existence of infinitely many weak solutions to the Kirchhoff-type equation.
Utilized specific conditions on the nonlinearity f(x,u) to ensure varied solutions.
Illustrated the findings with concrete examples showing practical relevance.

Abstract

In this paper, we investigate the existence of infinitely many solutions to the following nonlinear Kirchhoff-type equation: - (1+bₑ^₃ (| u|^2+V (x) u^2) \, dx) u+V (x) u=f (x, u) \ \ R^3, where b>0 is a constant, V (x) is a nonnegative potential, and the nonlinearity f (x, u) satisfies certain new local sublinear conditions. Using variational methods and a symmetric version of the mountain pass theorem, we establish the existence of infinitely many weak solutions. Several examples are provided to illustrate the applicability of our main results.

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