Second order Cauchy problem with a damping operator.
Second order differential inequalities in Banach spaces
We derive monotonicity results for solutions of ordinary differential inequalities of second order in ordered normed spaces with respect to the boundary values. As a consequence, we get an existence theorem for the Dirichlet boundary value problem by means of a variant of Tarski's Fixed Point Theorem.
Semiclassical states for weakly coupled nonlinear Schrödinger systems
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Semigroup structure underlying evolutions.
Semilinear evolution equations of the parabolic type
This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.
Semilinear fractional order integro-differential equations with infinite delay in Banach spaces
This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.
Semilinear integro-differential equations with compact semigroups.
Singular integral inequalities and stability of semilinear parabolic equations
Using a method developed by the author for an analysis of singular integral inequalities a stability theorem for semilinear parabolic PDEs is proved.
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Solutions of abstract hyperbolic equations by Rothe method.
Solutions to fractional differential equations with nonlocal initial condition in Banach spaces.
Solvability and asymptotic behavior of solutions of ordinary differential equations with variable operator coefficients
Solvability for a class of abstract two-point boundary value problems derived from optimal control.
Solvability of a multi-point boundary value problen of Neumann type.
Some applications of Zygmund's lemma to nonlinear differential equations in Banach and Hilbert spaces
Some compactness methods in the theory of nonlinear evolution equations with applications to P.D.E.
Some existence results for boundary value problems of fractional semilinear evolution equations.
Some remarks concerning a class of nonlinear evolution equations in Hilbert spaces
Some remarks on an operational time dependent equation
Some topological properties preserved by nearness between operators and applications to P.D.E.