On Linear and Nonlinear Fourth-Order Eigenvalue Problems with Nonlocal Boundary Condition

Abstract EN

We determine the principal eigenvalue of the linear problem u(4)(t)+βu′′(t)=μ[u(t)−u′′(t)], t∈(0,1), u(0)=u(1)=∫01p(s)u(s)ds, u′′(0)=u′′(1)=∫01q(s)u′′(s)ds, where 0<β<π2 and p,q∈L[0,1].

Moreover, we investigate the existence of positive solutions for the corresponding nonlinear problem.

The proofs of our main results are based upon the Krein-Rutman theorem and fixed point index theory.