SOLVABILITY OF HIGHER-ORDER BVPS IN THE HALF-LINE WITH UNBOUNDED NONLINEARITIES

This work presents suficient conditions for the existence of unbounded solutions of a Sturm-Liouville type boundary value problem on the half-line. One-sided Nagumo condition plays a special role because it allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on fixed point theory and lower and upper solutions method. An example is given to show the applicability of our results

Extremal points for impulsive Lidstone boundary value problems

The first extremal point for a boundary value problem with impulse for an nth-order linear, ordinary differential equation is characterized by the existence of a nontrivial solution that lies in a cone. Cone theoretic arguments are applied to linear, monotone, compacts maps. To construct such maps, an impulse effect operator is constructed to complement the usual Green's function approach. An application is made to a nonlinear problem

Eigenvalue problems for a conjugate difference equation

[[abstract]]We consider the third order difference equation ∆^3 y(k)+λF(k,y,∆y,∆^2y)=02≤k≤T+3 satisfying conjugate boundary conditions y(0)=y(1)=y(T+3)=0 Values of λ are characterized so that the boundary value problem has a positive solution.[[notice]]補正完

Existence of solutions for singular boundary problems for higher order differential equations

10.1007/BF02925259Rendiconti del Seminario Matematico e Fisico di Milano651249-26