Infinitely Many Positive Nonradial Solutions for the Kirchhoff Equation

ABSTRACT

We are concerned with the existence of positive nonradial solutions to the following Kirchhoff equation: where and are radial functions having the following expansions: with and . By introducing the Miranda theorem and developing some delicate analysis, we construct infinitely many positive nonradial multibump solutions of this equation under suitable numbers via the Lyapunov–Schmidt reduction method, whose maximum points lie on the top and bottom circles of a cylinder close to infinity. These nonradial multibump solutions are different from the ones obtained in a previous study. This result complements and extends the previous results in the literature.