Abstract This paper consider the existence and multiplicity of solutions for the first order Hamiltonian systems satisfying Sturm-Liouville boundary conditions without convexity assumption. The gradient of Hamiltonian function is generalized asymptotically linear. We find critical points of the corresponding functional by verifying the assumptions of Theorems about critical points given by Bart...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

In this paper, we study the nonlinear second-order impulsive qk-difference equations with Sturm-Liouville type, in which nonlinear team and impulsive teams are dependent on first-order qk-derivatives. We obtain the existence and uniqueness results of solutions for the problem by Banach’s contraction mapping principle and Schaefer’s fixed point theorems. Finally, we give two examples to demonstr...

The main aim of this paper is to construct quantum extension of the discrete Sturm–Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. ...

where the potentials are given functions. Under various boundary conditions, Sturm and Liouville established that solutions of problem (1) can exist only for particular values of the real parameter λ, which is called an eigenvalue. Relevant examples of linear Sturm-Liouville problems are the Bessel equation and the Legendre equation. The classical Sturm-Liouville theory does not depend upon the...