In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies ...In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function spaces.The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.展开更多
By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of applicat...By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of application are also given.展开更多
基金Deanship of Scientific Research at Majmaah University for supporting this work under Project Number No.R-1441-27.
文摘In this paper,we establish the existence of local stable manifolds for a semi-linear differential equation,where the linear part is a Hille-Yosida operator on a Banach space and the nonlinear forcing term f satisfies the ψ-Lipschitz conditions,where ψ belongs to certain classes of admissible function spaces.The approach being used is the fixed point arguments and the characterization of the exponential dichotomy of evolution equations in admissible spaces of functions defined on the positive half-line.
文摘By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of application are also given.
