tailieunhanh - báo cáo hóa học: " Periodic solutions for nonautonomous second order Hamiltonian systems with sublinear nonlinearity"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Periodic solutions for nonautonomous second order Hamiltonian systems with sublinear nonlinearity | Wang and Zhang Boundary Value Problems 2011 2011 23 http content 2011 1 23 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Periodic solutions for nonautonomous second order Hamiltonian systems with sublinear nonlinearity Zhiyong Wang 1 and Jihui Zhang2 Correspondence mathswzhy@ department of Mathematics Nanjing University of Information Science and Technology Nanjing 210044 Jiangsu People s Republic of China Full list of author information is available at the end of the article Springer Abstract Some existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems with sublinear nonlinearity by using the least action principle and minimax methods in critical point theory. Mathematics Subject Classification 2000 34C25 37J45 58E50. Keywords Control function Periodic solutions The least action principle Minimax methods 1 Introduction and main results Consider the second order systems iu t VF t u t . t e 0 T ị U 0 - u T u 0 - u T 0 where T 0 and F 0 T X RN R satisfies the following assumption A F t x is measurable in t for every x e RN and continuously differentiable in x for . t e 0 T and there exist a e C R R b e Lr 0 T R such that F t x a x t VF t x a x b t for all x e RN and . t e 0 T . The existence of periodic solutions for problem has been studied extensively a lot of existence and multiplicity results have been obtained we refer the readers to 1-13 and the reference therein. In particular under the assumptions that the nonlinearity VF t x is bounded that is there exists p t e L1 0 T R such that VF t x p t for all x e RN and . t e 0 T and that T ị F t x dt rc as x rc 0 Mawhin and Willem in 3 have proved that problem admitted a periodic solution. After that when the nonlinearity VF t x is sublinear that is there existsf t g t e L1 0 T R and a e 0 1 such that 2011 Wang and Zhang licensee Springer. This is an Open Access .