Simão Correia, Mário Figueira. Source: Advances in Differential Equations, Volume 24, Number 1/2, 1--30.Abstract: Consider the hyperbolic nonlinear Schrödinger equation $\mathrm {(HNLS)}$ over $\mathbb R^d$ $$ iu_t + u_{xx} - \Delta_{\textbf{y}} u + \lambda |u|^\sigma u=0. $$ We deduce the...
Marcelo Rempel Ebert, Wanderley Nunes do Nascimento. Source: Advances in Differential Equations, Volume 23, Number 11/12, 847--888.Abstract: In this paper, we study the long time behavior of energy solutions for a class of wave equation with time-dependent potential and speed of propagation. We...
Jaime Angulo Pava, Nataliia Goloshchapova. Source: Advances in Differential Equations, Volume 23, Number 11/12, 793--846.Abstract: The aim of this work is to demonstrate the effectiveness of the extension theory of symmetric operators in the investigation of the stability of standing waves for the...
Mamoru Okamoto. Source: Advances in Differential Equations, Volume 23, Number 9/10, 751--792.Abstract: We consider the long-time behavior of solutions to the fifth-order modified KdV-type equation. For the local-in-time well-posedness, we show that regularity conditions where by a tri-linear...
Isao Kato, Shinya Kinoshita. Source: Advances in Differential Equations, Volume 23, Number 9/10, 725--750.Abstract: We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension $d \ge 5$ with initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0} \in H^{s+1}(\mathbb{R}^d)...
Masashi Misawa, Nobumitsu Nakauchi. Source: Advances in Differential Equations, Volume 23, Number 9/10, 693--724.Abstract: In our previous papers, we introduce symphonic maps ([9]) and show a Hölder continuity of symphonic maps from domains of $\mathbb{R}^4$ into the spheres ([6], [7]). In this...
Yonggeun Cho, Gyeongha Hwang, Changhun Yang. Source: Advances in Differential Equations, Volume 23, Number 9/10, 649--692.Abstract: In this paper, we study 3-d Hartree type fractional Schrödinger equations: $$ i\partial_{t}u-\vert\nabla\vert^{\alpha}u = \lambda \left ( |x|^{-\gamma} *\vert...
Kanishka Perera, Cyril Tintarev, Jun Wang, Zhitao Zhang. Source: Advances in Differential Equations, Volume 23, Number 7/8, 615--648.Abstract: We study the existence of ground and bound state solutions for a system of coupled Schrödinger equations with linear and nonlinear couplings in...
Motohiro Sobajima, Yuta Wakasugi. Source: Advances in Differential Equations, Volume 23, Number 7/8, 581--614.Abstract: In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that...
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