Iterative solution of negative exponent Emden-Fowler problems.
The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term fractional...
In this paper, we consider the natural complex Hamiltonian systems with homogeneous potential , , of degree . The known results of Morales and Ramis give necessary conditions for the complete integrability of such systems. These conditions are expressed in terms of the eigenvalues of the Hessian matrix calculated at a non-zero point , such that . The main aim of this paper is to show that there are other obstructions for the integrability which appear if the matrix is not diagonalizable....
L’ingénieur belge Junius Massau (1852–1909) est considéré comme le créateur de l’intégration graphique. Il a mis au point des techniques élaborées de calcul par le trait pour construire avec précision les courbes intégrales des équations différentielles et, plus généralement, . Il s’est également penché sur l’intégration graphique des équations aux dérivées partielles. L’article se propose d’analyser ces travaux méconnus et de les replacer dans le contexte des mathématiques pratiquées par les...
By using monotone functionals and positive linear functionals on a suitable matrix space, new oscillation criteria for second order self-adjoint matrix differential systems with damping are given. The results are extensions of the Kamenev type oscillation criteria obtained by Wong for second order self-adjoint matrix differential systems with damping. These extensions also include an earlier result of Erbe et al.