Abstract

Using bifurcation method, we investigate the existence, nonexistence and multiplicity of positive solutions for the following Dirichlet problem involving mean curvature operator in Minkowski space $$\begin{aligned} \left\{ \begin{array}{lll} -\text {div}\left( \frac{\nabla v}{\sqrt{1-\vert \nabla v\vert ^2}}\right) = \lambda f(\vert x\vert ,v) &{}\quad \text {in}\,\, B_R(0),\\ v=0&{}\quad \text {on}\,\, \partial B_R(0). \end{array} \right. \end{aligned}$$ We managed to determine the intervals of the parameter \(\lambda \) in which the above problem has zero, one or two positive radial solutions corresponding to sublinear, linear, and superlinear nonlinearities f at zero respectively. We also studied the asymptotic behaviors of positive radial solutions as \(\lambda \rightarrow +\infty \).

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call