Vol.4 No.5 (September 2014)
Existence of Three Positive Solutions for a Class of Nonlinear Elliptic Systems
Motivated by existence of solutions of single equation, in this paper we study the existence of mul-tiple solutions of a class of nonlienar elliptic systems with nonhomogeneous boundary conditions. Using Guo-Krasnoselski’s fixed point theorem on cones, we prove that there exist at least three positive solutions for this class of nonlinear elliptic systems.
魏公明 , 陈雨彤 , 张兴丽 (2014) 一类非线性椭圆方程组三个正解的存在性。 理论数学， 4， 201-207. doi: 10.12677/PM.2014.45029
 Do, O.J.M., Lorcab, S. and Ubillac, P. (2005) Three positive radial solutions for elliptic equations in a ball. Applied Mathematics Letters, 18, 1163-1169.
 Ambrosetti, A. and Colorado, E. (2006) Bound and ground states of coupled nonlinear Schrodinger equations. Comptes Rendus de l’Académie des Sciences—Series I, 342, 453-458.
 Ambrosetti, A., Colorado, E. and Ruiz, D. (2007) Multi-bumb solitons to linearly coupled systems of nonlinear Schrodinger equations. Calculus of Variations and Partial Differential Equations, 30, 85-112.
 Ambrosetti, A. and Colorado, E. (2007) Standing waves of some coupled nonlinear Schrodinger equations. Journal London Mathematical Society, 75, 67-82.
 Torres, P.J. (2006) Guided waves in a multi-layered optical structure. Nonlinearity, 19, 2103-2113.
 Chu, J., O’regan, D. and Zhang, M. (2007) Positive solutions and eigenvalue intervals for nonlinear systems. Proceedings Mathematical Sciences, 117, 85-95.
 Krasnoselskii, M.A. (1964) Positive solutions of operator equation. Noordhoff, Groningen.
 Granas, A. and Dugundji, J. (2003) Fixed point theory. Springer, Berlin.
 Jiang, D., Wei, J. and Zhang, B. (2002) Positive periodic solutions of functional differential equations and population models. Electronic Journal of Differential Equations, 71, 1-13.
 Belmonte-Beitia, J., Perez-Garcia, V.M. and Torres, P.J. (2009) Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients. Journal of Nonlinear Science, 19, 437-451.