Oscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases

This paper deals with the prescribed mean curvature equations both in the Euclidean case and in the Lorentz-Minkowski case in presence of a nonlinearity $g$ such that $g'(0)>0$. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if $N=1$, while they are radial symmetric and decay to zero at infinity with their derivatives, if $N\ge 2$.Comment: 11 page

Singularly perturbed Neumann problems with potentials

We study the existence of concentrating solutions of a singularly perturbed Neumann problems with two potentials.Comment: 24 pages, 1 figur

Coupled nonlinear Schrodinger systems with potentials

Coupled nonlinear Schrodinger systems describe some physical phenomena such as the propagation in birefringent optical fibers, Kerr-like photorefractive media in optics and Bose-Einstein condensates. In this paper, we study the existence of concentrating solutions of a singularly perturbed coupled nonlinear Schrodinger system, in presence of potentials. We show how the location of the concentration points depends strictly on the potentials.Comment: 21 page

Interior spikes of a singularly perturbed Neumann problem with potentials

In this paper we prove that a singularly perturbed Neumann problem with potentials admits the existence of interior spikes concentrating in maxima and minima of an auxiliary function depending only on the potentials.Comment: 7 page

Locating the peaks of semilinear elliptic systems

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of $\Sigma$ in the sense of subdifferential calculus.Comment: To appear on Advanced Nonlinear Studies, 21 page