The main idea in this research is introducing another approximate method to calculate solutions of the fractional Torsion equation, which one applied equations civil engineering. Since order closed an integer, we convert equation a perturbed ordinary differential involving small parameter epsilon. Then can find exact and symmetries for alternative approximation equation. Also, with help definit...

We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary $\partial\Omega$ spatial domain $\Omega\subset\mathbb R^d$. On way, we first consider general symmetric order differential systems, for identify a new, large class potentials, called ensuring self-adjointness. Furthermore, using supersymmetric structure operator i...

we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation or the corresponding modified version play an important role in the study of the interface movements. In this work, we use the free software MAXIMA program symmgrp2009.max derived by W. Heremann to calculate the determining equations for the classical symm...

Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality. Particular cases are Dirac-Coulomb operators where distinguished selfadjoint extensions are obtained for the optimal range of coupling constants.

We have studied the self-adjointness of generalized MIC-Kepler Hamiltonian, obtained from the formally self-adjoint generalized MIC-Kepler Hamiltonian. We have shown that for l̃ = 0, the system admits an 1-parameter family of self-adjoint extension and for l̃ 6= 0 but l̃ < 1 2 , it has also an 1parameter family of self-adjoint extension.