arXiv subjects

Yanqiong Lu

Publications and source records attributed to Yanqiong Lu.

3 recordsLinked to original sources

arXiv2015

Proof of the Bonheure-Noris-Weth conjecture on oscillatory radial solutions of Neumann problems

Let $B_1$ be the unit ball in $\mathbb{R}^N$ with $N \geq 2$. Let $f\in C^1([0, \infty), \mathbb{R})$, $f(0)=0$, $f(β) = β, \ f(s) s\ \text{for}\ s\in (β, \infty)$ and $f'(β)>λ^{r}_k$. D. Bonheure, B. Noris and T. Weth [Ann. Inst. H. Poincaré Anal. Non Linéaire 29(4) (2012)] proved the existence of nondecreasing, radial positive solutions of the semilinear Neumann problem $$ -Δu+u=f(u) \ \text{in}\ B_1,\ \ \ \ \partial_νu=0 \ \text{on}\ \partial B_1 $$ for $k=2$, and they conjectured that there exists a radial solution with $k$ intersections with $β$ provided that $f'(β) >λ^r_k$ for $k>2$. In this paper, we show that the answer is yes.

math.AP↗

arXiv2015

On multiple positive ground state solutions for a mean curvature equation in Minkowski space

In this paper, we show how changes in the sign of nonlinearity leads to multiple radial ground state solutions of the mean curvature equation $ \nabla\cdot \Big[\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\Big] +λf(u)=0\ \ \text{in} \ \mathbb{R}^N $ for sufficiently large $λ$ with $N\geq 2$.

math.AP↗

arXiv2014

Global structure of radial positive solutions for a prescribed mean curvature problem in a ball

In this paper, we are concerned with the global structure of radial positive solutions of boundary value problem$$\text{div}\big(ϕ_{N}(\nabla v)\big)+λf(|x|, v)=0 \text{in} B(R), v=0 \text{on} \partial B(R), $$where $ϕ_{N}(y)=\frac{y}{\sqrt{1-|y|^{2}}}, y\in \mathbb{R}^{N}$, $λ$ is a positive parameter, $B(R)=\{x\in \mathbb{R}^{N} :|x|<R\}$, and $|\cdot|$ denote the Euclidean norm in $\mathbb{R}^{N}$. All results, depending on the behavior of nonlinear term $f$ near 0, are obtained by using global bifurcation techniques.

math.AP↗