Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

Patricio Felmer; Alexander Quaas; Jinggang Tan

doi:10.1017/S0308210511000746

Abstract

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We study the existence of positive solutions for the nonlinear Schrödinger equation with the fractional Laplacian

Furthermore, we analyse the regularity, decay and symmetry properties of these solutions.

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Chang, Xiaojun 2013. Ground state solutions of asymptotically linear fractional Schrödinger equations. Journal of Mathematical Physics, Vol. 54, Issue. 6,

Shen, Zifei and Gao, Fashun 2013. Existence of Solutions for a Fractional Laplacian Equation with Critical Nonlinearity. Abstract and Applied Analysis, Vol. 2013, Issue. , p. 1.

Shang, Xudong Zhang, Jihui and Yang, Yang 2013. On fractional Schr$\ddot{\mbox{o}}$ödinger equation in $\mathbb {R}^{N}$RN with critical growth. Journal of Mathematical Physics, Vol. 54, Issue. 12,

Zhao, Yang Cheng, De-Fu and Yang, Xiao-Jun 2013. Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System. Advances in Mathematical Physics, Vol. 2013, Issue. , p. 1.

Autuori, Giuseppina and Pucci, Patrizia 2013. Elliptic problems involving the fractional Laplacian inRN. Journal of Differential Equations, Vol. 255, Issue. 8, p. 2340.

Moroz, Vitaly and Van Schaftingen, Jean 2013. Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics. Journal of Functional Analysis, Vol. 265, Issue. 2, p. 153.

Shang, Xudong and Zhang, Jihui 2014. Ground states for fractional Schrödinger equations with critical growth. Nonlinearity, Vol. 27, Issue. 2, p. 187.

Felmer, Patricio and Torres, César 2014. Radial symmetry of ground states for a regional fractional Nonlinear Schrödinger Equation. Communications on Pure and Applied Analysis, Vol. 13, Issue. 6, p. 2395.

ZHANG, YONGCHAO and ZHU, GAOSHENG 2014. A POSITIVE SOLUTION FOR A NONLOCAL SCHRÖDINGER EQUATION. Bulletin of the Australian Mathematical Society, Vol. 90, Issue. 3, p. 469.

Dávila, Juan del Pino, Manuel and Wei, Juncheng 2014. Concentrating standing waves for the fractional nonlinear Schrödinger equation. Journal of Differential Equations, Vol. 256, Issue. 2, p. 858.

FELMER, PATRICIO and WANG, YING 2014. RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN. Communications in Contemporary Mathematics, Vol. 16, Issue. 01, p. 1350023.

Shen, Zifei and Gao, Fashun 2014. On the Existence of Solutions for the Critical Fractional Laplacian Equation inℝN. Abstract and Applied Analysis, Vol. 2014, Issue. , p. 1.

Fall, Mouhamed Moustapha and Valdinoci, Enrico 2014. Uniqueness and Nondegeneracy of Positive Solutions of $${(-\Delta)^s u + u = u^p \, {\rm in} \, \mathbb{R}^N}$$ ( - Δ ) s u + u = u p in R N when s is Close to 1. Communications in Mathematical Physics, Vol. 329, Issue. 1, p. 383.

Cho, Yonggeun Hajaiej, Hichem Hwang, Gyeongha and Ozawa, Tohru 2014. On the orbital stability of fractional Schrödinger equations. Communications on Pure & Applied Analysis, Vol. 13, Issue. 3, p. 1267.

Marinelli, Alessio and Mugnai, Dimitri 2014. The generalized logistic equation with indefinite weight driven by the square root of the Laplacian. Nonlinearity, Vol. 27, Issue. 9, p. 2361.

Wu, Dan 2014. Mass concentration phenomenon for inhomogeneous fractional Hartree equations. Journal of Mathematical Physics, Vol. 55, Issue. 11,

Secchi, Simone and Squassina, Marco 2014. Soliton dynamics for fractional Schrödinger equations. Applicable Analysis, Vol. 93, Issue. 8, p. 1702.

Jarohs, Sven and Weth, Tobias 2014. Asymptotic symmetry for a class of nonlinear fractional reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, Vol. 34, Issue. 6, p. 2581.

Wu, Dan 2014. Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity. Journal of Mathematical Analysis and Applications, Vol. 411, Issue. 2, p. 530.

Linares, Felipe Pilod, Didier and Saut, Jean-Claude 2014. Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory. SIAM Journal on Mathematical Analysis, Vol. 46, Issue. 2, p. 1505.

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Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian

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