Hugo Aimar, Ivana Gómez. Source: Annals of Functional Analysis, Advance publication, 13 pages.Abstract: We combine dyadic analysis through Haar-type wavelets (defined on Christ’s families of generalized cubes) and the Lax–Milgram theorem in order to prove the existence of Green’s functions for...
Raffaele Chiappinelli. Source: Annals of Functional Analysis, Advance publication, 10 pages.Abstract: We consider continuous gradient operators $F$ acting in a real Hilbert space $H$ , and we study their surjectivity under the basic assumption that the corresponding functional $\langle...
Alberto Lastra, Stéphane Malek. Source: Advances in Differential Equations, Volume 24, Number 1/2, 69--136.Abstract: We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter $\epsilon$. The problem possesses an irregular singularity in time at the origin and...
Yasuhide Fukumoto, Xiaopeng Zhao. Source: Advances in Differential Equations, Volume 24, Number 1/2, 31--68.Abstract: In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of electron inertia are studied. First, we establish the...
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...
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