Ground and bound states of periodic Schrodinger equations with super or asymptotically linear terms
Texas State University, Department of Mathematics
This paper is concerned with existence of ground and bound states for a class of nonlinear Schrodinger equation with periodic potential. We impose general assumptions on the nonlinearity with super or asymptotically linear growth, and find some refinements of known results and new results by using the perturbation method and a mountain pass argument. In particular, a critical point theory is established for the asymptotically linear growth case.
Schrödinger equations, Minimax characterization, Perturbation method, Nehari-Pankov manifold, Ground states
Wu, Q., & Qin, D. (2018). Ground and bound states of periodic Schrodinger equations with super or asymptotically linear terms. <i>Electronic Journal of Differential Equations, 2018</i>(25), pp. 1-26.