employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of neumann two-point boundary valuesturm-liouville type equations. using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

The Strum-Liouville equation is expressed in Hamiltonian form. A simple generating function is derived which defines a large class of canonical transformations and reduces the Sturm-Liouville equation to the solution of a first order equation with a single unknown. The method is developed with particular reference to the wave equation. The procedure unifies many apparently diverse treatments an...

A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained.

As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value condit...