28 research outputs found
Infinitely many periodic solutions for second order Hamiltonian systems
In this paper, we study the existence of infinitely many periodic solutions
for second order Hamiltonian systems , where is either asymptotically quadratic or superquadratic as .Comment: to appear in JDE(doi:10.1016/j.jde.2011.05.021
Ground state solutions for diffusion system with superlinear nonlinearity
In this paper, we study the following diffusion system
\begin{equation*}
\begin{cases}
\partial_{t}u-\Delta_{x} u +b(t,x)\cdot \nabla_{x} u +V(x)u=g(t,x,v),\\
-\partial_{t}v-\Delta_{x} v -b(t,x)\cdot \nabla_{x} v +V(x)v=f(t,x,u)
\end{cases}
\end{equation*}
where , and . Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth
Homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign nonlinearities
In this paper, we obtain the multiplicity of homoclinic solutions for a class of asymptotically autonomous Hamiltonian systems with indefinite sign potentials. The concentration-compactness principle is applied to show the compactness. As a byproduct, we obtain the uniqueness of the positive ground state solution for a class of autonomous Hamiltonian systems and the best constant for Sobolev inequality which are of independent interests
Homoclinic orbits for a class of nonperiodic Hamiltonian systems with some twisted conditions
In this paper, by the Masolv index theory, we will study the existence and
multiplicity of homoclinic orbits for a class of asymptotically linear
nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian
function