Solutions for a class of Hamiltonian systems on time scales with non-local boundary conditions

doi:10.1007/s10483-022-2832-9

Abstract

Abstract: In this work, the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions. The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems. Compared with the known results, this work establishes the variational structure in an appropriate Sobolev’s space. Then, by applying the mountain pass theorem and symmetric mountain pass theorem, the existence and multiplicity of the solutions are obtained. Finally, some examples with numerical simulation results are given to illustrate the correctness of the results obtained.

Key words: Hamiltonian system, non-local boundary condition, time scale, variational structure, critical point theory

2010 MSC Number:

34B15
58E50

Yongfang WEI, Suiming SHANG, Zhanbing BAI. Solutions for a class of Hamiltonian systems on time scales with non-local boundary conditions. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 587-602.

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