On sign-changing solutions for nonlinear operator equations

• DOI: 10.1016/j.jmaa.2006.04.064
• Publication Date: 2006-06-07T02:54:32Z
• Authors: Fuyi Li; Zhanping Liang; Qi Zhang; Yuhua Li
• Keywords: Operator (biology); Fixed-point index; Degree (music)

AbstractIn this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett–Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638–654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations.