Multiple nodal solutions to a scalar field equation with double-power nonlinearity and zero mass at infinity
Abstract
We consider the nonlinear elliptic equation $$\begin{aligned} -\Delta u + V(x)u = f(u), \qquad u\in D^{1,2}_0(\Omega ), \end{aligned}$$ in an exterior domain $$\Omega $$ of $$\mathbb {R}^N$$ , where V is a scalar potential that decays to zero at infinity and the nonlinearity f is subcritical at infinity and supercritical near the origin. Under weak symmetry assumptions, we provide conditions that guarantee that this problem has a prescribed number of sign-changing solutions. In particular, we show that in dimensions $$N\ge 4$$ there are numerous examples of exterior domains with finite symmetries in which the problem has a predetermined number of nodal solutions.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Navier-Stokes equation solutions
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 3
- Publication date
- 18 April 2026
- Language
- EN