Related papers: Monotone iterative technique for delayed evolution…
We show how the approach of Yosida approximation of the derivative serves to obtain new results for evolution systems. Using this method we obtain multivalued time dependent perturbation results. Additionally, translation invariant…
A strong inspiration for studying Sobolev type fractional evolution equations comes from the fact that have been verified to be useful tools in the modeling of many physical processes. We introduce a novel technique for solving Sobolev type…
The well established mixed monotone iterative technique that is used to study the existence and uniqueness of fractional order system is studied explicitly for impulsive system with Hilfer fractional order in this paper. The procedure of…
The global existence and stability of the solution to the delay differential equation (*)$\dot{u} = A(t)u + G(t,u(t-\tau)) + f(t)$, $t\ge 0$, $u(t) = v(t)$, $-\tau \le t\le 0$, are studied. Here $A(t):\mathcal{H}\to \mathcal{H}$ is a…
We consider a nonlinear implicit evolution inclusion driven by a nonlinear, nonmonotone, time-varying set-valued map and defined in the framework of an evolution triple of Hilbert spaces. Using an approximation technique and a surjectivity…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
Results of a previous paper [Commun. Contemp. Math., 09 (2007) 217-251] on the existence of solutions to a nonlinear evolution equation in an abstract Lebesgue space, arising from kinetic theory, are re-obtained in the more general setting…
In this paper, we consider the following general evolution equation $$ u_t=\Delta_fu+au\log^\alpha u+bu $$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of Souplet-Zhang type for positive smooth…
We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval $[0,1]$ endowed with a linear discontinuous production term, formulated in the space $\mathcal{M}([0,1])$ of…
This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs. The systematic design of these methods mixes the Runge-Kutta collocation formalism with…
Evolutionary algorithms (EAs) are general-purpose problem solvers that usually perform an unbiased search. This is reasonable and desirable in a black-box scenario. For combinatorial optimization problems, often more knowledge about the…
In the semigroup approach to stochastic evolution equations, the fundamental issue of uniqueness of mild solutions is often "reduced" to the much easier problem of proving uniqueness for strong solutions. This reduction is usually carried…
In this paper, we study the existence and uniqueness of pseudo $S$-asymptotically $\omega$-periodic mild solutions of class $r$ for fractional integro-differential neutral equations. An example is presented to illustrate the application of…
The main result of this research Monograph is the existence of small amplitude time quasi-periodic solutions for autonomous nonlinear wave equations $$ u_{tt} - \Delta u + V(x) u + g(x, u) = 0 \, , \quad x \in T^d \, , \quad g (x,u) = a(x)…
The purpose of this paper is to study stochastic evolution inclusions of the form \begin{align*} \eta(t,z) N_{\Theta}(dt \otimes z)\in dX(t)+\mathcal{A} X(t)dt, \end{align*} where $\mathcal{A}$ is a multi-valued operator acting on a…
The initial value problem for an evolution equation of type $v' + Av + BKv = f$ is studied, where $A:V_A \to V_A'$ is a monotone, coercive operator and where $B:V_B \to V_B'$ induces an inner product. The Banach space $V_A$ is not required…
We consider the nonlinear Klein-Gordon equation $\partial_t^2u(x,t)-\partial_x^2u(x,t)+\alpha u(x,t)=\pm|u(x,t)|^{p-1}u(x,t)$ on a periodic metric graph (necklace graph) for $p>1$ with Kirchhoff conditions at the vertices. Under suitable…
This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
We study the set of T-periodic solutions of a class of T-periodically perturbed Differential-Algebraic Equations with separated variables. Under suitable hypotheses, these equations are equivalent to separated variables ODEs on a manifold.…