Oscillating solutions for nonlinear Helmholtz equations

被引：1
作者：
Rainer Mandel
Eugenio Montefusco
Benedetta Pellacci
机构：
[1] Karlsruher Institut für Technologie,Institut für Analysis
[2] ”Sapienza” Università di Roma,Dipartimento di Matematica
[3] Università di Napoli ”Parthenope”,Dipartimento di Scienze e Tecnologie
来源：
Zeitschrift für angewandte Mathematik und Physik | 2017年 / 68卷
关键词：
Nonlinear Helmholtz equations; Standing waves; Oscillating solutions; 35J05; 35J20; 35Q55;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behaviour at infinity is established. Some generalizations to nonautonomous radial equations as well as existence results for nonradial solutions are found. Our theorems prove the existence of standing waves solutions of nonlinear Klein–Gordon or Schrödinger equations with large frequencies.
引用
收藏
相关论文
共 46 条
  • [1] Ambrosetti A(1994)Combined effects of concave and convex nonlinearities in some elliptic problems J. Funct. Anal. 122 519-543
  • [2] Brezis H(1995)A Dirichlet problem involving critical exponents Nonlinear Anal. 24 1639-1648
  • [3] Cerami G(1983)Équations de champs scalaires euclidiens non linéaires dans le plan C. R. Acad. Sci. Paris Sér. I Math. 297 307-310
  • [4] Boccardo L(1983)Nonlinear scalar field equations. I. Existence of a ground state Arch. Ration. Mech. Anal. 82 313-345
  • [5] Escobedo M(1986)Remarks on sublinear elliptic equations Nonlinear Anal. 10 55-64
  • [6] Peral I(2004)Criteria for the experimental observation of multidimensional optical solitons in saturable media Phys. Rev. E 70 046610-649
  • [7] Berestycki H(1997)Theory of incoherent self-focusing in biased photorefractive media Phys. Rev. Lett. 78 646-3015
  • [8] Gallouët T(2015)A dual approach in Orlicz spaces for the nonlinear Helmholtz equation Z. Angew. Math. Phys. 66 2995-502
  • [9] Kavian O(2017)Branch continuation inside the essential spectrum for the nonlinear Schrödinger equation J. Fixed Point Theory Appl. 19 475-388
  • [10] Berestycki H(2014)Real solutions to the nonlinear Helmholtz equation with local nonlinearity Arch. Ration. Mech. Anal. 211 359-728
12345