Some existence and multiplicity of homoclinic orbit for second order Hamiltonian system x-a(t)x + Wx(t, x)=0 are given by means of variational methods, where the potential V(t, x)=-a(t)|s|2 + W(t, s) is quadratic in s...Some existence and multiplicity of homoclinic orbit for second order Hamiltonian system x-a(t)x + Wx(t, x)=0 are given by means of variational methods, where the potential V(t, x)=-a(t)|s|2 + W(t, s) is quadratic in s at infinity and subquadratic in s at zero, and the function a(t) satisfies the growth condition lim→∞∫_t￣(t+l) a(t)dt=+∞,l∈R￣1.展开更多
Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
文摘Some existence and multiplicity of homoclinic orbit for second order Hamiltonian system x-a(t)x + Wx(t, x)=0 are given by means of variational methods, where the potential V(t, x)=-a(t)|s|2 + W(t, s) is quadratic in s at infinity and subquadratic in s at zero, and the function a(t) satisfies the growth condition lim→∞∫_t￣(t+l) a(t)dt=+∞,l∈R￣1.
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075109)
文摘Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.
