19 research outputs found
Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms
We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),yâČ(t),âŠ,y(q)(t))=0, tâ(0,1), y(k)(0)=0, 0â€kâ€mâ3, ζy(mâ2)(0)âΞy(mâ1)(0)=0, Ïy(mâ2)(1)+ÎŽy(mâ1)(1)=0 where mâ„3, 1â€qâ€mâ2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio