JNCA: Twin positive solutions for p-Laplacian nonlinear Neumann problems via variational and degree theoretical methodss



	Volume 9, Number 1, April 2008, pp. 1-23
Ravi P. Agarwaland, Michael E. Filippakis and Donal O'Regan Resmerita
Key words:
p-Laplacian, Neumann problem, (S )₊-operator, degree map, local minimizer, nonlinear Green's identity, homotopy invariance property.
Mathematices Subject Classification: Primary 35J60, 35J70.

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	Abstract:
	We consider a nonlinear Neumann problem driven by the p-Laplacian and with a nonsmooth potential function (hemivariational inequality). Using a combination of variational and degree theoretic techniques, we show that the problem has two positive smooth solutions. We also show the equivalence of W_n^1,p and C_n¹ minimizers for a large class of locally Lipschitz functionals.

Twin positive solutions for p-Laplacian nonlinear Neumann problems via variational and degree theoretical methodss