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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 9: Mathematics of Nonlinear Lattices
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Original Articles

Standing wave solutions of the discrete non-linear Schrödinger equations with unbounded potentials, II

Guoping Zhang Department of Mathematics, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21239, USACorrespondence[email protected]
&
Alexander Pankov Department of Mathematics, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21239, USA
Pages 1541-1557 | Received 02 Feb 2009, Accepted 27 Mar 2009, Published online: 18 Nov 2009

Citations (33)

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Read on this site (3)

Alexander Pankov & Guoping Zhang. (2022) Initial value problem of the discrete nonlinear Schrödinger equation with complex potential. Applicable Analysis 101:16, pages 5760-5774.
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Alexander Pankov. (2013) Standing waves for discrete nonlinear Schrödinger equations: sign-changing nonlinearities. Applicable Analysis 92:2, pages 308-317.
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Michael Herrmann. (2010) Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization. Applicable Analysis 89:10, pages 1591-1602.
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Articles from other publishers (30)

Guoping Zhang & Ghder Aburamyah. (2024) Global attractor and l^p solutions to initial value problems of discrete nonlinear Schrodinger equations complex potential. Electronic Journal of Differential Equations 2024:01-??, pages 12.
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Guoping Zhang. (2023) The spectrum theory of the discrete Schrödinger operator and its application. Malaya Journal of Matematik 11:S, pages 125-148.
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Zhenguo Wang & Qiuying Li. (2023) Standing Waves Solutions for the Discrete Schrödinger Equations with Resonance. Bulletin of the Malaysian Mathematical Sciences Society 46:5.
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Qilin Xie & Huafeng Xiao. (2023) Normalized solutions for the discrete Schrödinger equations. Boundary Value Problems 2023:1.
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Meihua Huang & Zhan Zhou. (2023) The existence of discrete solitons for the discrete coupled nonlinear Schrödinger system. Boundary Value Problems 2023:1.
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Qilin Xie & Huafeng Xiao. (2022) Infinitely many solutions for the discrete Schrödinger equations with a nonlocal term. Boundary Value Problems 2022:1.
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Dirk Hennig, Nikos I. Karachalios & Jesús Cuevas-Maraver. (2022) The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation. Journal of Differential Equations 316, pages 346-363.
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Guanwei Chen & Martin Schechter. (2022) Multiple solutions for Schrödinger lattice systems with asymptotically linear terms and perturbed terms. Discrete & Continuous Dynamical Systems - B 27:4, pages 2107.
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Guanwei Chen & Jijiang Sun. (2021) Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems. Boundary Value Problems 2021:1.
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Guanwei Chen & Shiwang Ma. (2021) Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions. Calculus of Variations and Partial Differential Equations 60:5.
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Qilin Xie. (2021) Solutions for discrete Schrödinger equations with a nonlocal term. Applied Mathematics Letters 114, pages 106930.
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Guanwei Chen & Martin Schechter. (2021) Multiple homoclinic solutions for discrete Schrödinger equations with perturbed and sublinear terms. Zeitschrift für angewandte Mathematik und Physik 72:2.
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Liqian Jia & Guanwei Chen. (2021) Non-periodic discrete Schrödinger equations with sign-changing and super-quadratic terms: Existence of solutions. Journal of Applied Analysis & Computation 11:1, pages 242-253.
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Guanwei Chen & Martin Schechter. (2019) Multiple solutions for non-periodic Schrödinger lattice systems with perturbation and super-linear terms. Zeitschrift für angewandte Mathematik und Physik 70:5.
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Guanwei Chen & Shiwang Ma. (2018) Perturbed Schrödinger lattice systems: existence of homoclinic solutions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149:04, pages 1083-1096.
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Guanwei Chen & Martin Schechter. (2019) Non-periodic Schrödinger lattice systems with perturbed and asymptotically linear terms: Negative energy solutions. Applied Mathematics Letters 93, pages 34-39.
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Qilin Xie. (2019) Multiple solutions for the nonhomogeneous discrete nonlinear Schrödinger equation. Applied Mathematics Letters 91, pages 144-150.
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Tie-shan He, Meng Zhang, Kai-hao Liang & Peng-fei Guo. (2019) Standing Waves for Discrete Nonlinear Schrödinger Equations with Nonperiodic Bounded Potentials. Acta Mathematicae Applicatae Sinica, English Series 35:2, pages 374-385.
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Lynn Erbe, Baoguo Jia & Qinqin Zhang. (2019) HOMOCLINIC SOLUTIONS OF DISCRETE NONLINEAR SYSTEMS VIA VARIATIONAL METHOD. Journal of Applied Analysis & Computation 9:1, pages 271-294.
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Liqian Jia, Jun Chen & Guanwei Chen. (2017) Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions. Advances in Difference Equations 2017:1.
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Liqian Jia & Guanwei Chen. (2017) Discrete Schrödinger equations with sign-changing nonlinearities: Infinitely many homoclinic solutions. Journal of Mathematical Analysis and Applications 452:1, pages 568-577.
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Liqian Jia & Guanwei Chen. (2016) Multiple solutions of discrete Schrödinger equations with growing potentials. Advances in Difference Equations 2016:1.
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Guanwei Chen & Martin Schechter. (2016) Non-periodic discrete Schrödinger equations: ground state solutions. Zeitschrift für angewandte Mathematik und Physik 67:3.
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Mustafa Avci & Alexander Pankov. (2015) Nontrivial solutions of discrete nonlinear equations with variable exponent. Journal of Mathematical Analysis and Applications 431:1, pages 22-33.
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Zhan Zhou & DeFang Ma. (2014) Multiplicity results of breathers for the discrete nonlinear Schrödinger equations with unbounded potentials. Science China Mathematics 58:4, pages 781-790.
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Ming Cheng. (2015) Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping. Journal of Function Spaces 2015, pages 1-7.
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Ali Mai & Zhan Zhou. (2014) Homoclinic Solutions for a Class of Nonlinear Difference Equations. Journal of Applied Mathematics 2014, pages 1-8.
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Guowei Sun. (2013) On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations. Abstract and Applied Analysis 2013, pages 1-6.
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Defang Ma & Zhan Zhou. (2012) Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials. Abstract and Applied Analysis 2012, pages 1-15.
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A. Pankov & G. Zhang. (2011) Standing wave solutions for discrete nonlinear Schrödinger equations with unbounded potentials and saturable nonlinearity. Journal of Mathematical Sciences 177:1, pages 71-82.
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