An Elliptic Neumann Problem with Subcritical Nonlinearity
Volume 53 / 2005
Bulletin Polish Acad. Sci. Math. 53 (2005), 7-16 MSC: 35B33, 35B38, 35J35, 35J60, 35J65, 35Q55. DOI: 10.4064/ba53-1-2
We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.