Nakao Hayashi, Pavel I. Naumkin. Source: Advances in Differential Equations, Volume 25, Number 1/2, 31--80.Abstract: We consider the Cauchy problem for the fractional nonlinear Schrödinger equation \[ \left\{ \begin{array} [c]{c}% i\partial_{t}u+\frac{1}{\alpha} \left| \partial_{x} \right|...
Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki. Source: Advances in Differential Equations, Volume 25, Number 1/2, 1--30.Abstract: In this article, we prove two versions of the Lyapunov center theorem for symmetric potentials. We consider a second order autonomous system $$ \ddot...
Eudes Mendes Barboza, João Marcos do Ó, Bruno Ribeiro. Source: Advances in Differential Equations, Volume 24, Number 11/12, 713--744.Abstract: In this paper, our goal is to study the following class of Hénon type problems \begin{equation*} \left\{\begin{array}{rclcl}\displaystyle -\Delta u &...
Mitsuo Higaki. Source: Advances in Differential Equations, Volume 24, Number 11/12, 647--712.Abstract: The asymptotic stability of two-dimensional stationary flows in a non-symmetric exterior domain is considered. Under the smallness condition on initial perturbations, we show the stability of the...
Norihisa Ikoma, Kazunaga Tanaka. Source: Advances in Differential Equations, Volume 24, Number 11/12, 609--646.Abstract: We study the existence of $L^2$ normalized solutions for nonlinear Schrödinger equations and systems. Under new Palais-Smale type conditions, we develop new deformation...
Takeyuki Nagasawa, Kohei Nakamura. Source: Advances in Differential Equations, Volume 24, Number 9/10, 581--608.Abstract: Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the...
Tomoyuki Tanaka. Source: Advances in Differential Equations, Volume 24, Number 9/10, 555--580.Abstract: We consider the Cauchy problem of third order Benjamin-Ono type equations on the torus. Nonlinear terms may yield derivative losses, which prevents us from using the classical energy method. In...
Fabio Camilli, Raul De Maio. Source: Advances in Differential Equations, Volume 24, Number 9/10, 531--554.Abstract: We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving...
Jie Xiao, Dachun Yang, Junjie Zhang, Yuan Zhou. Source: Advances in Differential Equations, Volume 24, Number 9/10, 501--530.Abstract: This paper shows a Liouville-type law for the incompressible Stokes system and a trace principle over the uniform domains for the BMO-Q spaces...
Carlos Esteve, Philippe Souplet. Source: Advances in Differential Equations, Volume 24, Number 7/8, 465--500.Abstract: We consider a well-known model for micro-electromechanical systems (MEMS) with variable dielectric permittivity, involving a parabolic equation with singular nonlinearity. We...
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