论文信息 - On Some Discrete Variational Problems

On Some Discrete Variational Problems

Making use of a discrete version of the P.-L. Lions concentration-compactness principle, we establish some results on the existence of nontrivial solutions for nonlinear stationary discrete equations of the Schrödinger type.

Alexander Pankov | A. Pankov | N. Zakharchenko | N. Zakharchenko

[1] A. Pankov. Semilinear elliptic equations in ℝn with nonstabilizing coefficients , 1989 .

[2] D. Hennig,et al. Wave transmission in nonlinear lattices , 1999 .

[3] Pierre-Louis Lions,et al. Nonlinear scalar field equations, I existence of a ground state , 1983 .

[4] P. Lions. The concentration-compactness principle in the calculus of variations. The locally compact case, part 1 , 1984 .

[5] A. Pankov,et al. On a semilinear Schro¨dinger equation with periodic potential , 1998 .

[6] W. Rother,et al. Nonlinear scalar field equations , 1992, Differential and Integral Equations.

[7] P. Lions. The concentration-compactness principle in the Calculus of Variations , 1984 .

[8] C. V. Coffman. On a class of non-linear elliptic boundary value problems , 1969 .

[9] Alexander Pankov,et al. Bounded and Almost Periodic Solutions of Nonlinear Operator Differential Equations , 1990 .

[10] Zeev Nehari,et al. Characteristic values associated with a class of nonlinear second-order differential equations , 1961 .