This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asympt...This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asymptotically periodic and satisfy0<a≤α(x), 0<γ(x)≤B, -M≤β(x)≤M.A positive homoclinic orbit of the equation is obtained by means of variational methods.展开更多
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 existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x+f(t,x)=0 are given by means of variational methods, where the function -1/2a（t）|s|^2∫^t0f（t,s）ds is asymptotically ...Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x+f(t,x)=0 are given by means of variational methods, where the function -1/2a（t）|s|^2∫^t0f（t,s）ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t+1 t a（t）dt=+∞，VI∈R^1.A resonance case as well as a noncompact case is discussed too.展开更多
This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lo...This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lower order perturbation of u(n+2)/(n--2) at infinity.展开更多
文摘This note studies the existence of positive homoclinic orbits of the second order equation-u″+α(x)u=β(x)u q+γ(x)u p, x∈R,where 1<q<p.Assume that the coefficient functions α(x),β(x) and γ(x) are asymptotically periodic and satisfy0<a≤α(x), 0<γ(x)≤B, -M≤β(x)≤M.A positive homoclinic orbit of the equation is obtained by means of variational methods.
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.
文摘Some existence and multiplicity of homoelinic orbits for second order Hamiltonian system x-a(t)x+f(t,x)=0 are given by means of variational methods, where the function -1/2a（t）|s|^2∫^t0f（t,s）ds is asymptotically quadratic in s at infinity and subquadratic in s at zero, and the function a (t) mainly satisfies the growth condition limt→∞∫^t+1 t a（t）dt=+∞，VI∈R^1.A resonance case as well as a noncompact case is discussed too.
文摘This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lower order perturbation of u(n+2)/(n--2) at infinity.
