60 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)+ÎťF(t,y(t),yâ˛(t),âŚ,y(q)(t))=0, tâ(0,1), y(k)(0)=0, 0â¤kâ¤mâ3, Îśy(mâ2)(0)âθy(mâ1)(0)=0, Ďy(mâ2)(1)+δy(mâ1)(1)=0 where mâĽ3, 1â¤qâ¤mâ2, and Îť>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 Îť 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
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