Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbric...Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.展开更多
This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L(t)z+Wz(t,z)=0,where L∈C(R,RN2)is a symmetric matrix-valued function and W(t,z)∈C1(R×RN,R)is a...This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L(t)z+Wz(t,z)=0,where L∈C(R,RN2)is a symmetric matrix-valued function and W(t,z)∈C1(R×RN,R)is a nonlinear term.Since there are no periodic assumptions on L(t)and W(t,z)in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W(t,z)is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.展开更多
文摘Let k be a commutative ring, C a projective k-coalgebra. The smash productsof entwining structure (A, C)_ψ are discussed. When the map ψ is a bijective, and C is a finitelygenerated k-module, a version of the Ulbrich theorem for coalgebras C is given.
文摘This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L(t)z+Wz(t,z)=0,where L∈C(R,RN2)is a symmetric matrix-valued function and W(t,z)∈C1(R×RN,R)is a nonlinear term.Since there are no periodic assumptions on L(t)and W(t,z)in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W(t,z)is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.