Radial and nonradial minimizers for some radially symmetric functionals.
Uniqueness of a symmetric positive solution to an ODE system.
Stability of peakons for the generalized Camassa-Holm equation.
Nonlocal variational problems arising in long wave propagation
Instability of radial standing waves of Schrödinger equation on the exterior of a ball.
Nonlocal variational problems arising in long wave propagatioN
In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness...
Solitary waves for some nonlinear Schrödinger systems
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