Existence theory for nonlinear Volterra integral and differential equations.
Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration...
Existence, uniqueness and regularity for Kruzkov's solutions of the Burger-Carleman's system
Existenz der Wellenoperatoren für eine allgemeine Klasse von Operatoren.
Expanding the applicability of two-point Newton-like methods under generalized conditions
We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied....
Expansion of an atomic operator.
Expansional in banach algebras
Expansions and eigenfrequencies for damped wave equations
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds,...
Expansions in Generalized Eigenfunctions of Selfadjoint Operators.
Explicit representation of compact linear operators in Banach spaces via polar sets
We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.
Explicit solution for an infinite dimensional generalized inverse eigenvalue problem.
Explicit solutions for boundary value problems related to the operator equations
Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation are studied for the general case, even when the algebraic equation is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.
Explicit solutions for non homogeneous Sturm-Liouville operators problems.
In this paper we study existence and sufficiency conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X'' - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given.
Explicit solutions for Sturm-Liouville operator problems (II).
It is proved that the resolution problem of a Sturm-Liouville operator problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of the corresponding algebraic operator equation. Existence and uniqueness conditions for the existence of nontrivial solutions of the problem and explicit expressions of them are given.
Exponential and polynomial dichotomies of operator semigroups on Banach spaces
Let A generate a C₀-semigroup T(·) on a Banach space X such that the resolvent R(iτ,A) exists and is uniformly bounded for τ ∈ ℝ. We show that there exists a closed, possibly unbounded projection P on X commuting with T(t). Moreover, T(t)x decays exponentially as t → ∞ for x in the range of P and T(t)x exists and decays exponentially as t → -∞ for x in the kernel of P. The domain of P depends on the Fourier type of X. If R(iτ,A) is only polynomially bounded, one obtains a similar result with polynomial...
Exponential bounds for noncommuting systems of matrices
It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form . The proof appeals to the monogenic functional calculus.
Exponential decay law and irreversibility of decay and collision processes
Exponential dichotomy and strongly stable vectors of Hilbert space contraction semigroups
Exponential dichotomy for evolution families on the real line.
Exponential dichotomy of difference equations in -phase spaces on the half-line.