1,721,004 research outputs found
A multiplicity result for solutions of a nonlinear elliptic system with Neumann conditions
No full textOscillating solutions for prescribed mean curvature equations: Euclidean and Lorentz-Minkowski cases
No full textThis paper deals with the prescribed mean curvature equations − div 1± ∇u |∇u| 2 = g(u) in RN , both in the Euclidean case, with the sign “+”, and in the Lorentz-Minkowski case, with the sign “−”, for N 1 under the assumption g(0) > 0. 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 2
Singularly perturbed Neumann problems with potentials
No full textThe main purpose of this paper is to study the existence of single-peaked solutions of the
Neumann problem
\cases
-\varepsilon^2 \text{\rm div} \left(J(x)\nabla u\right)+V(x)u=u^p
& \text{in }\Omega,
\\
\displaystyle \dfrac{\partial u}{\partial \nu}=0
& \text{on }\partial\Omega,
\endcases
where is a smooth bounded domain of \{\mathbb R}^N, , and
and are positive bounded scalar value potentials.
We will show that, for the existence of concentrating solutions, one has to check if at least one
between and is not constant on . In this case the concentration
point is determined by and only. In the other case the concentration
point is determined by an interplay among the derivatives of and calculated on
and the mean curvature of
Ground states for a system of nonlinear Schrödinger equations with three wave interaction
No full textWe consider a system of nonlinear Schrödinger equations with three wave interaction studying the existence of ground state solutions. In particular, we find a vector ground state, namely, a ground state (u1,u2,u3) such that ui≠0 for all i = 1, 2, 3
Oscillating solutions for nonlinear equations involving the Pucci's extremal operators
No full textThis paper deals with the following nonlinear equations Mλ,Λ ±(D2u)+g(u)=0inRN,where Mλ,Λ ± are the Pucci's extremal operators, for N⩾1 and under the assumption g′(0)>0. 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⩾2
A Variational Analysis of a Gauged Nonlinear Schrödinger Equation.
Full text linkThis paper is motivated by a gauged Schrodinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem
-Delta u(x) + (omega + h(2)(vertical bar x vertical bar) /vertical bar x vertical bar(2) + integral(infinity)(vertical bar x vertical bar) h(s)/s u(2)(s) ds )u(x) = vertical bar u(x)vertical bar(p-1) u(x),
where
h(r) = 1/2 integral(r)(0) su(2)(s) ds.
This problem is the Euler-Lagrange equation of a certain energy functional. We study the global behavior of that functional. We show that for p is an element of (1.3), the functional may be bounded from below or not, depending on omega. Quite surprisingly, the threshold value for omega is explicit. From this study we prove existence and non-existence of positive soluti
On a "zero mass" nonlinear Schrödinger equation
No full textWe look for positive solutions to the nonlinear Schrödinger equation -ε2Δu - V(x)f′ (u) = 0 in RN, where V is a continuous bounded positive potential and f satisfies particular growth conditions which make our problem fall in the so called "zero mass case". We prove an existence result for any ε > 0, and a multiplicity result for ε sufficiently small
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