[PDF] Top 20 On an initial boundary value problem for the nonlinear Schrödinger equation

... an existence and uniqueness result for the damped problem holding for arbitrary initial values.. For this purpose we start from.[r] ... See full document

... This paper is organized as follows. In Sect. 2, definitions and properties of Mittag-Leffler functions and fractional integrals and derivatives are presented. In Sect. 3, we consider the fractional wave equation (1) ... See full document

... and nonlinear alternative of Leray-Schauder type in a ...this problem by a fixed-point theorem in partially ordered ...the boundary value problem of the fractional differential equations ... See full document

... modified Schrödinger-type identity related to the Schrödinger-type boundary value problem with mixed boundary conditions and spatial ... See full document

... the problem is interest- ing in ...differential equation, the properties of its solutions such as the existence, multiplicity, and uniqueness may not be shared between the continuous differential ... See full document

... We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at ... See full document

... This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the ... See full document

... Partial differential equations, piecewise constant delay, boundary value problem, initial value problem, abstract Cauchy problem, Hilbert space, loaded equation, wave equation.. 1991 AMS[r] ... See full document

... It follows that F ∈ H  l–s (–γ , K h ∞ ) ⊂ H – l–s– (–γ , K h ∞ ). Because the strip m + l – s –  – n  ≤ Im λ ≤ m + l – s – n  does not contain spectral points of problem (.)-(.), then using results in ... See full document

... In this section we deal with main theorem of existence of global week solution. By using these lemmas and using the Gross logarithmic Sobolev inequality with the combination of Galerkin method to construct approximate ... See full document

... particular initial and boundary data are ...similar problem to (P1) is presented: the heat source F depends on the temperature on the fixed face x = 0 when a heat flux boundary condition is ... See full document

... of nonlinear Schrödinger differential ...integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz ... See full document

... Brenner and von Wahl 20 proved the existence and uniqueness of classical solutions to the initial boundary problem for 1.1 in Hilbert space. Pecher 21 investigated the existence and uniqueness of ... See full document

... the initial boundary value problems of equations with or without nonlocal boundary conditions; see [–] and references ...the initial boundary value problem for a ... See full document

... Some authors have studied the global finiteness of the solutions[3,4] and blow up properties of the solutions[9] with various boundary conditions to the equations and systems of evolutionary Laplacian equations. ... See full document

... study initial-boundary value problem for an equation of composite type in 3-D multiply connected ...This equation governs nonsteady inertial waves in rotating ...the ... See full document

... completely determined. As a result, the solution u(x) of the Volterra integral equation (II.3) in a series form is readily obtained by using the series assumption in (II.4). It is clearly seen that the ... See full document

... the Schrödinger-type identity related to the sin- gular boundary value ...ary value problem for the Schrödinger equation was ... See full document

... the initial-boundary value problems in one space vari- able, which involve an integral over the spatial domain of a function of the desired solution that may appear in a boundary ...heat ... See full document

... the initial boundary value problem of ...large initial data. In , Ikehata [] investigated the initial boundary value problem of ...plate ... See full document