We consider the nonlinear stationary Schrödinger equation− Δu+ V (x) u= f (x, u) in RN. Here
f is a superlinear, subcritical nonlinearity, and we mainly study the case where both V and f …

Consider the semilinear Schrödinger equation (*) -Δu+V(x)u=f(x,u), u∈H^1(R^N). It is
shown that if f, V are periodic in the x-variables, f is superlinear at u=0 and ±∞ and 0 lies in a …

arxiv:math/0404450v3 [math.AP] 5 May 2004 Periodic Nonlinear Schrödinger Equation with
Application to Photonic Crystals Page 1 arxiv:math/0404450v3 [math.AP] 5 May 2004 Periodic …

This unique book focuses on critical point theory for strongly indefinite functionals in order to
deal with nonlinear variational problems in areas such as physics, mechanics and …

STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS
Page 1 Reviews in Mathematical Physics Vol. 20, No. 8 (2008) 1007–1032 c World Scientific …

In [9], Floer and Weinstein considered (1.1) when N= 1, p= 3 and V (x) is a bounded function
and has a nondegenerate critical. They used a Lyapunov-Schmidt type reduction to prove …

We consider the Schrödinger equation-Δ u+ V (x) u= f (x, u), where V is periodic and f
asymptotically periodic in the x-variables, 0 is in a spectral gap of-Δ+ V and f is either …

We analyze the existence, stability, and internal modes of gap solitons in nonlinear periodic
systems described by the nonlinear Schrödinger equation with a sinusoidal potential, such …

(NS){−∆ u+ V (x) u= g (x, u) for x∈ RN; u (x)→ 0 as| x|→∞; where V and g are assumed to be
periodic in x. The spectrum σ (S) of S=−∆+ V on L2 (RN) is purely absolutely continuous. We …

(1.1) dAu-u+ uv O, u> 0 du/dv 0 on df, where I) is a bounded smooth domain in RN, N> 2,
and v is the unit outer normal to tf; d> 0, p> 1 are constants; and p is subcritical, ie, p<(N+ …