Differential and Integral Equations

Nodal solutions to problem with mean curvature operator in Minkowski space

Guowei Dai and Jun Wang

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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

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

First available in Project Euclid: 18 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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