Global bifurcation and nodal solutions of N-dimensional p- Laplacian in unit ball

Abstract

We are concerned with determining values of γ, for which there exist radial nodal solutions of the boundary-value problem

where B is the unit open ball in ℝ ^N with N ≥ 1. The proofs of our main results are based upon bifurcation techniques. In particular, we establish the global bifurcation theory for a second-order weighted p-Laplacian eigenvalue problem in B.

Keywords:

• nodal solutions
• eigenvalue
• bifurcation
• unit ball

AMS Subject Classifications::

• 35B05
• 35B32
• 35J25

Acknowledgements

The authors are very grateful to the anonymous referees for their valuable suggestions. This research was supported by the NSFC (No. 11061030, No. 10971087), NWNU-LKQN-10-21.