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Bull. Korean Math. Soc. 2014; 51(1): 99-113
Printed January 1, 2014
https://doi.org/10.4134/BKMS.2014.51.1.99
Copyright © The Korean Mathematical Society.
Multiple solutions for a $p$-Laplacian system with nonlinear boundary conditions
Jun Zhou and Chan-Gyun Kim
Southwest University, College of William and Mary
A nonlinear elliptic problem involving $p$-Laplacian and nonlinear boundary condition is considered in this paper. By using the method of Nehari manifold, it is proved that the system possesses two nontrivial nonnegative solutions if the parameter is small enough.
Keywords: $p$-Laplacian systems, nonlinear boundary condition, multiple solutions, Nehari manifold
MSC numbers: 35J50, 35J57, 35J66
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