Nodal Solution for a Kirchhoff-Type Problem in R<sup><i>N</i></sup>

• 作者: Leilei Sha
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Sign-Changing Solutions NONLOCAL Operator Kirchhoff-Type Equations
• 年，卷（期）: 2020,（1）
• 页码范围: 42-52
• 页数: 11页
• 分类号: O17

摘要

In this paper, we study the existence of nodal solutions of the following general Schödinger-Kirchhoff type problem: where a,b > 0, N ≥ 3, g : R → R+ is an even differential function and g''(s) ≥ 0 for all s ≥ 0, h : R → R is an odd differential function. These equations are related to the generalized quasilinear Schödinger equations: Because the general Schödinger-Kirchhoff type problem contains the nonlocal term, it implies that the equation (KP1) is no longer a pointwise identity and is very different from classical elliptic equations. By introducing a variable replacement, we first prove that (KP1) is equivalent to the following problem: whereand G-1 is the inverse of G. Next, we prove that (KP2) is equivalent to the following system with respect to : For every integer k > 0, radial solutions of (KP1) with exactly k nodes are obtained by dealing with the system (S) under some appropriate assumptions. Moreover, this paper established the nonexistence results if N ≥ 4 and b is sufficiently large.