scholarly journals Ground states for superlinear fractional Schrödinger equations in R^N

2016 ◽  
Vol 41 ◽  
pp. 745-756 ◽  
Author(s):  
Vincenzo Ambrosio
Keyword(s):  
Ground States ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Fractional Schrödinger Equations

Ground states for fractional Schrödinger equations involving a critical nonlinearity

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
Xia Zhang ◽  
Binlin Zhang ◽  
Mingqi Xiang
Keyword(s):  
Critical Exponents ◽  
Ground States ◽  
Real Parameter ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Critical Nonlinearity ◽  
Fractional Schrödinger Equations

AbstractThis paper is aimed to study ground states for a class of fractional Schrödinger equations involving the critical exponents:where λ is a real parameter,

scholarly journals On fractional Schrödinger equations with Hartree type nonlinearities

2021 ◽  
Vol 4 (6) ◽  
pp. 1-33
Author(s):  
Silvia Cingolani ◽  
◽  
Marco Gallo ◽  
Kazunaga Tanaka ◽  
Keyword(s):  
Fractional Laplacian ◽  
Riesz Potential ◽  
Ground States ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Asymptotic Decay ◽  
General Solutions ◽  
Nonlocal Equation ◽  
Fractional Schrödinger Equations

<abstract><p>Goal of this paper is to study the following doubly nonlocal equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document} $(- \Delta)^s u + \mu u = (I_\alpha*F(u))F'(u) \quad {\rm{in}}\;{\mathbb{R}^N}\qquad\qquad\qquad\qquad ({\rm{P}}) $ \end{document} </tex-math> </disp-formula></p> <p>in the case of general nonlinearities $ F \in C^1(\mathbb{R}) $ of Berestycki-Lions type, when $ N \geq 2 $ and $ \mu &gt; 0 $ is fixed. Here $ (-\Delta)^s $, $ s \in (0, 1) $, denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential $ I_{\alpha} $, $ \alpha \in (0, N) $. We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in <sup>[<xref ref-type="bibr" rid="b23">23</xref>,<xref ref-type="bibr" rid="b61">61</xref>]</sup>.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document