On the existence of soliton solutions to quasilinear Schrödinger equations

Keywords

Nabla symbol, Mathematics, Nonlinear system, Minimax, Mathematical physics

References

• Existence and multiplicity results for some superlinear elliptic problems on RNThomas Bartsch, Zhiqiang Wang — 1995
• Variational methods for nonlinear elliptic eigenvalue problemsFelix E. Browder — 1965
• Dual variational methods in critical point theory and applicationsAntonio Ambrosetti, Paul H. Rabinowitz — 1973
• Relativistic self-focusing and channel formation in laser-plasma interactions.Burke Ritchie — 1994
• On the Local Well Posedness of Quasilinear Schrödinger Equations in Arbitrary Space DimensionMarkus Poppenberg — 2001
• Nonlinear electromagnetic-spin wavesF. G. Bass — 1990
• Large-Amplitude Quasi-Solitons in Superfluid FilmsSusumu Kurihara — 1981
• On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potentialYong‐Geun Oh — 1990
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potentialAndreas Floer, Alan Weinstein — 1986
• Relativistic and ponderomotive self‐focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximationH. S. Brandi, C. Manus, G. Mainfray — 1993
• Global Existence of Small Solutions to a Relativistic Nonlinear Schrödinger EquationAnne de Bouard, Nakao Hayashi, Jean‐Claude Saut — 1997
• A general method for the solution of nonlinear soliton and kink Schrödinger equationsRainer W. Hasse — 1980
• EXISTENCE AND SYMMETRY OF MULTI-BUMP SOLUTIONS FOR NONLINEAR SCHRODINGER EQUATIONSZhi-Qiang Wang — 1999
• Evolution theorem for a class of perturbed envelope soliton solutionsE. W. Laedke, Karl‐Heinz Spatschek, L. Stenflo — 1983
• Upper‐hybrid solitons and oscillating‐two‐stream instabilitiesM. Porkoláb, M. V. Goldman — 1976
• Equation of motion for the Heisenberg spin chainG. Quispel, H.W. Capel — 1981
• Existence of solitary waves in higher dimensionsWalter A. Strauss — 1977
• Minimax methods in critical point theory with applications to differential equationsP. Rabinowitz — 1986
• Nonlinear scalar field equations, I existence of a ground stateHenri Berestycki, P. L. Lions — 1983
• Classical Planar Heisenberg Ferromagnet, Complex Scalar Field and Nonlinear ExcitationsSachio Takeno, Shigeo Homma — 1981

Cited by

• Positive solutions to a class of quasilinear elliptic equations on RAntonio Ambrosetti, Zhi-Qiang Wang — 2003
• Solutions for a quasilinear Schr"odinger equation: a dual approachMathieu Colin, Louis Jeanjean — 2004
• A class of quasilinear Schrödinger equations with critical or supercritical exponentsYoujun Wang — 2015
• Métodos variacionais aplicados a uma classe de equações de Schrödinger quasilinearesGilberto Vieira — 2011
• G-invariant positive solutions for a quasilinear Schrödinger equationShinji Adachi, Tatsuya Watanabe — 2011
• Soliton solutions for quasilinear Schrödinger equations, IJiaquan Liu, Zhi-Qiang Wang — 2002
• Multiple solutions for a class of quasilinear Schrödinger equations in ℝNCaisheng Chen — 2015
• Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equationsYinbin Deng, Shuangjie Peng, Shusen Yan — 2016
• Asymptotic uniqueness of ground states for a class of quasilinear Schrödinger equations with H 1 -supercritical exponentShinji Adachi, Tatsuya Watanabe — 2016
• Quasilinear elliptic equations with critical growth via perturbation methodXiangqing Liu, Jiaquan Liu, Zhi-Qiang Wang — 2013
• Sharp condition of global existence for second-order derivative nonlinear Schrödinger equations in two space dimensions☆Ji Shu, Jian Zhang — 2007
• Existence of Nontrivial Solutions and High Energy Solutions for a Class of Quasilinear Schrödinger Equations via the Dual-Perturbation MethodYu Chen, Xian Wu — 2013
• Uniqueness of the ground state solutions of quasilinear Schrödinger equationsShinji Adachi, Tatsuya Watanabe — 2012
• On a class of periodic quasilinear Schrödinger equations involving critical growth in R2Abbas Moameni — 2006
• Nodal soliton solutions for quasilinear Schrödinger equations with critical exponentYinbin Deng, Shuangjie Peng, Jixiu Wang — 2013
• Sharp conditions of global existence for the quasilinear Schrödinger equationJ. Zhang, Ji Shu — 2008
• Existence and concentration of ground states to a quasilinear problem with competing potentialsWenbo Wang, Xianyong Yang, Fukun Zhao — 2014
• Multiple solutions for quasilinear Schrödinger equations with a parameterXian Wu — 2014
• Existence of solutions for a general quasilinear elliptic system via perturbation methodYujuan Jiao, Shengmao Fu, Yanli Wang — 2013
• Bifurcations for quasilinear Schrödinger equations, IJiaquan Liu, Inbo Sim, Zhi-Qiang Wang — 2007

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