## Differential and Integral Equations

- Differential Integral Equations
- Volume 30, Number 5/6 (2017), 463-480.

### Nodal solutions to problem with mean curvature operator in Minkowski space

Guowei Dai and Jun Wang

#### Abstract

This paper is devoted to investigate the existence and multiplicity of radial nodal solutions for the following Dirichlet problem with mean curvature operator in Minkowski space \begin{eqnarray} \begin{cases} -\text{div} \Big (\frac{\nabla v}{\sqrt{1-\vert \nabla v\vert^2}} \Big ) = \lambda f(\vert x\vert,v)\,\, &\text{in}\,\, B_R(0),\\ v=0~~~~~~~~~~~~~~~~~~~~~~\,\,&\text{on}\,\, \partial B_R(0). \end{cases} \nonumber \end{eqnarray} By bifurcation approach, we determine the interval of parameter $\lambda$ in which the above problem has two or four radial nodal solutions which have exactly $n-1$ simple zeros in $(0,R)$ according to linear/sublinear/ superlinear nonlinearity at zero. The asymptotic behaviors of radial nodal solutions as $\lambda \to +\infty$ and $n \to +\infty$ are also studied.

#### Article information

**Source**

Differential Integral Equations, Volume 30, Number 5/6 (2017), 463-480.

**Dates**

First available in Project Euclid: 18 March 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1489802422

**Mathematical Reviews number (MathSciNet)**

MR3626584

**Zentralblatt MATH identifier**

06738557

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations 34C23: Bifurcation [See also 37Gxx] 35B40: Asymptotic behavior of solutions 34C10: Oscillation theory, zeros, disconjugacy and comparison theory

#### Citation

Dai, Guowei; Wang, Jun. Nodal solutions to problem with mean curvature operator in Minkowski space. Differential Integral Equations 30 (2017), no. 5/6, 463--480. https://projecteuclid.org/euclid.die/1489802422