Existence of solutions for the multipoint boundary value problems for p(t)-Laplacian system
ZHANG Qi-hu1,2, YANG Jin3, CUI Zhi-hui3
(1 College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China; 2 Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, Jiangsu, China;3 Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China)
Abstract:
Investigates the existence of solutions for multipoint boundary value problems for the one dimensional p(t)-Laplacian system via Leray-Schauder degree. When the nonlinear term f(t,u) satisfies sub-p- growth conditions with respect to u, the existence of solutions for this problem is proved. If the nonlinear term f(t,u)=σ(t)|u|q(t)-2u+ρ(t) and satisfies super-p+ growth conditions with respect to u, the sufficient conditions for the existence of solutions for this problem is obtained, when |ρ|0+|e| is small enough.
KeyWords:
p(t)-Laplacian; Leray-Schauder degree; fixed point
