Coupled System of Boundary Value Problems

In this chapter we shall investigate the existence of positive solutions of the coupled system of boundary value problem $$u'' + f(t,\nu ) = 0$$ (11.1) $$\nu '' + g(t,u) = 0$$ (11.1) $$\left\{ {\begin{array}{*{20}{c}}{{\alpha _1}u(0) - {\beta _1}u''(0) = 0} \\{{\gamma _1}u(1) + {\delta _1}u''(1) = 0}\end{array}} \right.$$ (11.2) $$\left\{ {\begin{array}{*{20}{c}}{{\alpha _2}\nu (0) - {\beta _2}\nu ''(0) = 0} \\{{\gamma _2}\nu (1) + {\delta _2}\nu ''(1) = 0}\end{array}} \right.$$ (11.2) where α i ≥ 0, β i ≥ 0, γ i ≥ 0, δ i ≥ 0, ρ i = γ i β i +α i γ i +α i δ i > 0, i = 1, 2.