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Homoclinic trajectories and chaotic behaviour in a piecewise linear oscillator
(2007)In this paper we consider the equation " x + x = sin(v root 2t) + s( x), where s( x) is a piece wise linear map given by min{5x, 1} if x = 0 and by max{ 1, 5x} if x < 0. The existence of chaotic behaviour in the Smale ... 
An eigenvalue problem for a quasilinear elliptic field equation on R^n
(2001)We study the field equation −Δu+V(x)u+εr(−Δpu+W′(u))=μu on Rn, with ε positive parameter. The function W is singular in a point and so the configurations are characterized by a topological invariant: the topological ... 
Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold
(2008)The relation between the number of solutions of a nonlinear equation on a Riemannian manifold and the topology of the manifold itself is studied. The technique is based on LjusternikSchnirelmann category and Morse theory. ... 
Multiplicity of symmetric solutions for a nonlinear eigenvalue problem in ℝn
(2005)In this paper, we study the nonlinear eigenvalue field equation Δu + V(x)u + ε(Δu + W′(u)) = μu where u is a function from ℝ to ℝ with n ≥ 3, ε is a positive parameter and p > n. We find a multiplicity of solutions, ... 
Solitary waves solutions of a nonlinear Schroedinger equation
(Birkhaeuser, 2003)The aim of this note is to prove the existence of standing waves solutions of the following nonlinear Schrödinger equation I(∂ψ/∂t)=−Δψ+V(x)ψ+εN(ψ), where NM is a nonlinear differential operator. In [8] and [9] Benci and ... 
An eigenvalue problem for a quasilinear elliptic field equation
(Elsevier, 2001)We study the field equation Deltau + V(x)u + epsilon (Delta (p)u + W'(u)) = mu mu on a bounded domain and on Rn, with E positive parameter. The function W is singular in a point and so the configurations are characterized ... 
On the number of blowingup solutions to a nonlinear elliptic equation with critical growth
(2007)In this paper we estimate the number of solutions to {Δω + V(x)ω = n(n  2)ω in R ω > 0 in R ω ∈ D(R) which blow up at a suitable critical point of the potential V as the parameter ∈ goes to zero. Copyright © 2007 Rocky ...