EXISTENCE OF POSITIVE SOLUTION FOR A SIXTH–ORDER BEAM EQUATION WITH VARIABLE PARAMETERS

This paper investigates the existence of positive solutions for the sixth-order boundary value problem with three variable parameters: −u⁽⁶⁾ + A(t)u⁽⁴⁾ + B(t)u′′ + C(t)u = uφ + f(t, u, u′′), 0 < t < 1 −φ′′ + λφ = µg(t, u(t)), 0 < t < 1 u(0) = u(1) = u′′(0) = u′′(1) = u(4)(0) = u(4)(1) = φ(0) = φ(1) = 0, where µ is a positive parameter. The existence of the positive solution depends on µ, i.e. there exists a positive number µ such that if 0 < µ < µ the BVP has a positive solution. Using a fixed point theorem and an operator spectral theorem we give some new existence results.