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Three solutions for a nonlinear Neumann boundary value problem

Najib Tsouli, Omar Chakrone, Omar Darhouche, Mostafa Rahmani (2014)

Applicationes Mathematicae

The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form - Δ p ( x ) u + a ( x ) | u | p ( x ) - 2 u = μ g ( x , u ) in Ω, | u | p ( x ) - 2 u / ν = λ f ( x , u ) on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.

Transversal biwave maps

Yuan-Jen Chiang, Robert A. Wolak (2010)

Archivum Mathematicum

In this paper, we prove that the composition of a transversal biwave map and a transversally totally geodesic map is a transversal biwave map. We show that there are biwave maps which are not transversal biwave maps, and there are transversal biwave maps which are not biwave maps either. We prove that if f is a transversal biwave map satisfying certain condition, then f is a transversal wave map. We finally study the transversal conservation laws of transversal biwave maps.

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