An Eigenvalue Problem for Quasilinear Systems
Johnny Henderson, Haiyan Wang · Rocky Mountain Journal of Mathematics · 2007
The paper deals with the existence of positive solutions for the n-dimensional quasilinear system (Φ(u )) + λh(t)f (u) = 0, 0 < t < 1, with the boundary condition u(0) = u(1) = 0.The vector-valued function Φ is defined by Φ(u) = (ϕ(u 1 ), . . ., ϕ(u n )), where u = (u 1 , . . ., u n ), and ϕ covers the two important cases ϕ(u) = u and ϕ(uWe prove that the boundary value problem has a positive solution, for certain finite intervals of λ, if one of f 0 and f ∞ is large enough and the other one is small enough.Our methods employ fixed point theorems in a cone.