A comparison between the fourth order linear differential equation with its boundary value problem

Abstract

In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).

Keywords

• linear differential equation
• eigenvalue
• eigenfunction
• upper bound
• linearly independent solution
• wrongskian