Schrödinger equations with concave and convex nonlinearities

  • Zhaoli Liu
  • Zhi-Qiang Wang
Original Paper

DOI: 10.1007/s00033-005-3115-6

Cite this article as:
Liu, Z. & Wang, ZQ. Z. angew. Math. Phys. (2005) 56: 609. doi:10.1007/s00033-005-3115-6

Abstract.

We obtain the existence of infinitely many nodal solutions for the Schrödinger type equation on \(\mathbb{R}^N : - \Delta u + V(x)u = f(x,u)\) with \(u \in H^1 (\mathbb{R}^N ).\) Here, \(V \in C(\mathbb{R}^N ,\mathbb{R}),\,V(x) \geq 1,\int_{\mathbb{R}^N } {(V(x))^{ - 1} dx < + \infty .} \) The nonlinearity f is symmetric in the sense of being odd in u, and may involve a combination of concave and convex terms.

Mathematics Subject Classification (2000).

35J2035J60

Keywords.

Schrödinger equationnonlinearity with concave and convex termsnodal solutioninvariant set

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  • Zhaoli Liu
    • 1
  • Zhi-Qiang Wang
    • 2
    • 3
  1. 1.Department of MathematicsCapital Normal UniversityBeijingP.R. China
  2. 2.Department of Mathematics and StatisticsUtah State UniversityLoganUSA
  3. 3.School of Mathematics and Computer SciencesFujian Normal UniversityFuzhouP.R. China