We prove the existence of equivariant finite time blow-up solutions for the wave map
problem from ℝ 2+ 1→ S 2 of the form u(t,r)=Q(λ(t)r)+R(t,r) where u is the polar angle on the …

Abstract Given ν> 1/2 and δ> 0 arbitrary, we prove the existence of energy solutions of∂ tt
u− Δ u− u 5= 0 (0. 1) in R 3+ 1 which blow up exactly at r= t= 0 as t→ 0−. These solutions are …

The notion of an invariant manifold arises naturally in the asymptotic stability analysis of
stationary or standing wave solutions of unstable dispersive Hamiltonian evolution …

We systematically develop Weyl-Titchmarsh theory for singular differential operators on
arbitrary intervals $(a, b)\subseteq\mathbb {R} $ associated with rather general differential …

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 …

This book introduces and discusses the self-adjoint extension problem for symmetric
operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman …

We give a comprehensive treatment of Sturm-Liouville operators whose coefficients are
measures, including a full discussion of self-adjoint extensions and boundary conditions …

The paper is devoted to operators given formally by the expression-∂ _x^ 2+\left (α-1
4\right) 1 x^ 2.-∂ x 2+ α-1 4 1 x 2. This expression is homogeneous of degree minus 2 …

We consider the critical focusing wave equation (-∂ _t^ 2+ Δ) u+ u^ 5= 0 in R^ 1+ 3 and
prove the existence of energy class solutions which are of the form u (t, x)= t^ μ 2 W (t^ μ x)+ …

We develop Weyl–Titchmarsh theory for Schrödinger operators with strongly singular
potentials such as perturbed spherical Schrödinger operators (also known as Bessel …