In this paper, we present a detailed study of class sixth-order semilinear PDEs: existence, regularity and uniqueness. The uniqueness results are consequence maximum principle called the P-function method.

This paper deals with the solution behavior and periodic nature of solutions difference equation $$ s_{n+1}=\alpha s_{n}+\dfrac{\beta s_{n}s_{n-4}}{\gamma s_{n-4}+\delta s_{n-5} },\;\;\;n=0,1,... {\Large \noindent }where initial conditions $s_{-5},\ s_{-4},\ s_{-3},\ s_{-2},\ s_{-1},\ s_{0}$ are arbitrary positive real numbers $\alpha ,\ \beta \gamma \delta \ $are constants. Also we obtain clos...

We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.

The zeros of the eigenfunctions of self-adjoint Sturm–Liouville eigenvalue problems interlace. For these problems interlacing is crucial for completeness. For the complex Sturm–Liouville problem associated with the Schrödinger equation for a non-Hermitian PT-symmetric Hamiltonian, completeness and interlacing of zeros have never been examined. This paper reports a numerical study of the Sturm– ...

We show how a number of NP-complete as well as NP-hard problems can be reduced to the Sturm-Liouville eigenvalue problem in the quantum setting with queries. We consider power queries which are derived from the propagator of a system evolving with a Hamiltonian obtained from the discretization of the Sturm-Liouville operator. We use results of our earlier paper concering the complexity of the S...