Advances in Differential Equations
- Adv. Differential Equations
- Volume 11, Number 12 (2006), 1375-1396.
Existence of minimal nodal solutions for the nonlinear Schrödinger equations with $V(\infty)=0$
We consider the problem $\Delta u+V(x)u=f'(u)$ in $\mathbb R^N$. Here the nonlinearity has a double power behavior and $V$ is invariant under an orthogonal involution, with $V(\infty)=0$. An existence theorem of one pair of solutions which changes sign exactly once is given.
Adv. Differential Equations Volume 11, Number 12 (2006), 1375-1396.
First available in Project Euclid: 18 December 2012
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Mathematical Reviews number (MathSciNet)
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35D05 35J20: Variational methods for second-order elliptic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)
Ghimenti, M.; Micheletti, A. M. Existence of minimal nodal solutions for the nonlinear Schrödinger equations with $V(\infty)=0$. Adv. Differential Equations 11 (2006), no. 12, 1375--1396. https://projecteuclid.org/euclid.ade/1355867589.