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 …

The aim of this book is to give a modern presentation of the spectral and scattering theory for
Sturm–Liouville equations, including some results on inverse theory. We plan a second …

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 …

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

The Inverse Spectral Transform for the Conservative Camassa–Holm Flow with Decaying Initial
Data Page 1 Digital Object Identifier (DOI) 10.1007/s00205-016-1066-z Arch. Rational Mech …

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 …

We consider one-dimensional Dirac operator LP, U with Birkhoff regular boundary
conditions and summable potential P (x) on [0, π]. We introduce strongly and weakly regular …

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 …

This article is concerned with the isospectral problem− f ″+ 1 4 f= z ω f+ z 2 υ f for the
periodic conservative Camassa–Holm flow, where ω is a periodic real distribution in H loc …