Construction of nonradial solutions for fractional critical equation with weaker symmetrical function
Abstract
We consider the following fractional critical equation with weaker symmetrical function:$ \begin{align} \begin{cases} (-\Delta)^{s}u = K(|y'|, y'')u^{2_s^*-1}, \hbox{ }u>0, &\hbox{ }y\in B_1(0), \\ u = 0, &\hbox{ } y\in B_{1}^{c}(0), \end{cases} \end{align}~~~~~(0.1) $where $ 2_s^* = \frac{2N}{N-2s} $, $ K(y) = K(|y'|, y'') $ is a bounded function defined in $ \mathbb{R}^{2} \times \mathbb{R}^{N-2} $ for $ y = (y', y''), y'\in \mathbb{R}^2, y''\in \mathbb{R}^{N-2} $, and $ B_1(0) $ is the unit ball in $ \mathbb{R}^{N}. $ We show that if $ K(y) $ satisfies some suitable conditions, then equation (0.1) has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 52
- Issue
- 0
- Pages
- 342–371
- Publication date
- 1 January 2026
- Language
- EN