The existence of nontrivial solutions of Kirchhoff type equations is an important nonlocal
quasilinear problem; in this paper we use minimax methods and invariant sets of descent …

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 …

This 2003 book presents min-max methods through a study of the different faces of the
celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. The reader is led …

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a
periodic potential; in particular, the localized modes supported by the periodic potential. It …

Abstract Let G=(V, E) be a locally finite graph, whose measure μ (x) has positive lower
bound, and Δ be the usual graph Laplacian. Applying the mountain-pass theorem due to …

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 …

In this paper a quasi-linear elliptic equation in the whole Euclidean space is considered. The
nonlinearity of the equation is assumed to have exponential growth or have critical growth in …

(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 …