Differential and Integral Equations

Schrödinger type equations with asymptotically linear nonlinearities

Zhi-Qiang Wang and Francois A. van Heerden

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We study the nonlinear Schrödinger type equation $$-\Delta u~+~(\lambda g(x)~+~1)u~=~f(u)$$ on the whole space ${{\mathbf R}^N}$. The nonlinearity $f$ is assumed to be asymptotically linear and $g(x)\geq 0$ has a potential well. We do not assume a limit for $g(x)$ as $|x|\to\infty$. Using variational techniques, we prove the existence of a positive solution for $\lambda$ large. In the case where $f$ is odd we obtain multiple pairs of solutions. The limiting behavior of solutions as $\lambda\to\infty$ is also considered.

Article information

Source
Differential Integral Equations, Volume 16, Number 3 (2003), 257-280.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060671

Mathematical Reviews number (MathSciNet)
MR1947953

Zentralblatt MATH identifier
0476.03047

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

van Heerden, Francois A.; Wang, Zhi-Qiang. Schrödinger type equations with asymptotically linear nonlinearities. Differential Integral Equations 16 (2003), no. 3, 257--280. https://projecteuclid.org/euclid.die/1356060671


Export citation