Existence Of Homoclinic Orbits For A Class Of Hamiltonian Systems

In the 19th century,the British mathematician Hamilton proposed the Hamiltonian system and was widely used in the fields of biology and physics.In the 1970s,based on the variational method,after the establishment of critical point theory,many researchers began to discuss the existence of system solutions in the field of mathematics and achieved a lot of outstanding results.This paper proves the existence of homoclinic solutions of Hamiltonian systems,by researching equation using the variational method and the topological degree theorem.The first chapter mainly introduces the Hamiltonian system and its development history,as well as some existing achievements of the Hamiltonian system with the same orbit.Chapter 2 introduces the definition of the.degree of decomposition and the spectral decomposition of the self-adjoint operator used in the proof process.In the third chapter,the existence of homoclinic orbits for a class of Hamiltonian systems is proved.