Multi-bump solutions to Kirchhoff type equations in the plane with the steep potential well vanishing at infinity

In this paper, we study the following Kirchhoff type equation with a steep potential well vanishing at infinity: -(a + b integral(R2)|del u|(2)dx) Delta u + (h(x) + mu V (x))u = K(x) f(u) in R-2, where a, b > 0 are constants, mu > 0 is a parameter, V decays to zero at infinity as |x|(-gamma )with gamma is an element of (0 , 2] and int V (-1)(0) possesses multiple disjoint bounded components. We prove the existence of multi-bump solutions for mu > 0 large enough and the concentration behavior of multi-bump solutions as mu -> +infinity. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.