Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most
famously the Camassa–Holm shallow water wave equation. These solutions take the form of …

The aim of this paper is to develop an analytical approach to obtain the sharp estimates for
the lowest positive periodic eigenvalue and all Dirichlet eigenvalues of a general Sturm …

In this paper, we present a short proof of the maximization of Dirichlet eigenvalue ratios for
the Camassa–Holm equation y′′= 1 4 y+ λ m (x) y, by solving the infinitely dimensional …

The aim of this paper is to obtain the optimal characterizations of locations for all nodes of
the classical Sturm-Liouville operators, given the L p norms with 1< p<∞ of the potentials …

MINIMIZATION OF LOWEST POSITIVE PERIODIC EIGENVALUE FOR CAMASSA-HOLM
EQUATION WITH INDEFINITE POTENTIAL 1. Introduction It is we Page 1 MINIMIZATION OF …

Generalized indefinite strings provide a canonical model for self-adjoint operators with
simple spectrum (other classical models are Jacobi matrices, Krein strings and 2× 2 …

Given two measures μ, ν and their total variations, we study the minimization of Neumann
eigenvalues for measure differential equation dy•= y (t) d μ (t)+ λ yd ν (t). By solving the …

The aim of this paper is to obtain the sharp estimate for the lowest positive eigenvalue for the
Camassa-Holm equation y ″= 1 4 y+ λ m (t) y, with the Neumann-Dirichlet boundary …

In this paper we are concerned with the spectral problem (y 1 y 2) x=(− 1 2 1 2 λ m− 1 2 λ m
1 2)(y 1 y 2) for the periodic generalized Camassa-Holm equations. The first aim is to study …

We study the Lyapunov stability of the periodic generalized Camassa–Holm equation in
terms of the periodic/anti-periodic eigenvalues and the associated spectral intervals …