منابع مشابه
Multi - Bump Solutions on Lattices
We consider the following semi-linear elliptic equation with critical exponent: −∆u = K(x)u n+2 n−2 , u > 0 in R, where n ≥ 3, K > 0 is periodic in (x1, ..., xk) with 1 ≤ k < n−2 2 . Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in R, including infinite lattices. We also show tha...
متن کاملMulti-Bump Orbits Homoclinic to Resonance Bands∗
We establish the existence of several classes of multi-bump orbits homoclinic to resonance bands for completely-integrable Hamiltonian systems subject to small-amplitude Hamiltonian or dissipative perturbations. Each bump is a fast excursion away from the resonance band, and the bumps are interspersed with slow segments near the resonance band. The homoclinic orbits, which include multi-bump Ši...
متن کاملExistence and Symmetry of Multi-bump Solutions for Nonlinear Schrr Odinger Equations
We study the existence and symmetry property of multi-bump solutions of Especially when the potential V is radially symmetric, multi-bump solutions are constructed with bumps concentrating on a single connected component of the set of global minimum points of V. Furthermore, conditions are given to assure that the multi-bump solutions obtained have prescribed subgroups of O(N) as their exact sy...
متن کاملSign-changing Multi-bump Solutions for Nonlinear Schrödinger Equations with Steep Potential Wells
We study the nonlinear Schrödinger equations: (Pλ) −∆u+(λa(x)+1)u = |u|p−1u, u ∈ H(R ), where p > 1 is a subcritical exponent, a(x) is a continuous function satisfying a(x) ≥ 0, 0 < lim inf |x|→∞ a(x) ≤ lim sup|x|→∞ a(x) < ∞ and a−1(0) consists of 2 connected bounded smooth components Ω1 and Ω2. We study the existence of solutions (uλ) of (Pλ) which converge to 0 in RN \ (Ω1 ∪Ω2) and to a presc...
متن کاملMulti-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generaliz...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(02)00346-3