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May/June 2017 Nodal solutions to problem with mean curvature operator in Minkowskispace
Guowei Dai, Jun Wang
Differential Integral Equations 30(5/6): 463-480 (May/June 2017).

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.

Citation

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Guowei Dai. Jun Wang. "Nodal solutions to problem with mean curvature operator in Minkowskispace." Differential Integral Equations 30 (5/6) 463 - 480, May/June 2017.

Information

Published: May/June 2017
First available in Project Euclid: 18 March 2017

zbMATH: 06738557
MathSciNet: MR3626584

Subjects:
Primary: 34C10, 34C23, 35B40, 35J65

Rights: Copyright © 2017 Khayyam Publishing, Inc.

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Vol.30 • No. 5/6 • May/June 2017
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