The main purpose of this paper is to investigate existence of transversal homoclinic orbits of nonlinear system of two small parameters in a degenerate case. By making use ofthe theory of exponential dichotomy and Lia...The main purpose of this paper is to investigate existence of transversal homoclinic orbits of nonlinear system of two small parameters in a degenerate case. By making use ofthe theory of exponential dichotomy and Liapunov-Schmidt method, we construct Melnikov-like functions, and show that if these functions satisfy some conditions thentransversal homoclinic orbits of nonlinear system exists.展开更多
文摘The main purpose of this paper is to investigate existence of transversal homoclinic orbits of nonlinear system of two small parameters in a degenerate case. By making use ofthe theory of exponential dichotomy and Liapunov-Schmidt method, we construct Melnikov-like functions, and show that if these functions satisfy some conditions thentransversal homoclinic orbits of nonlinear system exists.
