Existence and regularity for semilinear parabolic evolution equations
Existence and uniqueness of mild solutions of second order Volterra integrodifferential equations with nonlocal conditions.
Existence and uniqueness of solutions to a semilinear functional-differential evolution nonlocal Cauchy problem.
Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations.
Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces.
Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations.
Existence of solutions for a second order abstract functional differential equation with state-dependent delay.
Existence of solutions for an abstract second-order differential equation with nonlocal conditions.
Existence of solutions for semilinear differential equations with nonlocal conditions in Banach spaces.
Existence of solutions for semilinear nonlocal Cauchy problems in Banach spaces.
Existence of solutions in the -norm for partial differential equations of neutral type with finite delay.
Existence of solutions of a second order abstract functional Cauchy problem with nonlocal conditions
We establish the existence of mild, strong, classical solutions for a class of second order abstract functional differential equations with nonlocal conditions.
Existence of solutions to a second order partial differential equation with nonlocal conditions.
Existence of solutions to neutral differential equations with deviated argument.
Existence of solutions to quasilinear functional differential equations.
Existence of the fundamental solution of a second order evolution equation
We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence of bounded operators.
Existence results for a second-order abstract Cauchy problem with nonlocal conditions.
Existence results for impulsive neutral functional differential equations with state-dependent delay.
Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces.
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...