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 Multiple solutions for a $p$-Laplacian system with nonlinear boundary conditions Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 99-113 https://doi.org/10.4134/BKMS.2014.51.1.99Printed January 1, 2014 Jun Zhou and Chan-Gyun Kim Southwest University, College of William and Mary Abstract : 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 Downloads: Full-text PDF