scholarly journals A BLOW-UP METHOD TO PROVE FORMAL INTEGRABILITY FOR SOME PLANAR DIFFERENTIAL SYSTEMS

2018 ◽  
Vol 8 (6) ◽  
pp. 1833-1850
Keyword(s):  
Blow Up ◽  
Differential Systems ◽  
Formal Integrability

BLOW-UP PHENOMENA PROFILE FOR HADAMARD FRACTIONAL DIFFERENTIAL SYSTEMS IN FINITE TIME

Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950093 ◽  
Author(s):  
LI MA
Keyword(s):  
Banach Space ◽  
Lipschitz Condition ◽  
General Condition ◽  
Finite Time ◽  
Blow Up ◽  
Differential Systems ◽  
Functional Operator ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Theoretical Results

The main purpose of this paper is to investigate the weak singularity of solutions for some nonlinear Hadamard fractional differential systems (HFDSs). By constructing proper Banach space and employing lower and upper solutions technique, we prove the existence of the blow-up solutions for a class of HFDSs. In addition, we establish a more general condition than the classical Lipschitz condition which is employed to guarantee the equivalence between the solutions to HFDS and the corresponding functional operator. Also several examples are presented to verify our theoretical results.

scholarly journals On the Formal Integrability Problem for Planar Differential Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Antonio Algaba ◽  
Cristóbal García ◽  
Jaume Giné
Keyword(s):  
Algebraic Curves ◽  
Necessary Conditions ◽  
Differential Systems ◽  
Analytic Integrability ◽  
Integrability Problem ◽  
Formal Integrability

We study the analytic integrability problem through the formal integrability problem and we show its connection, in some cases, with the existence of invariant analytic (sometimes algebraic) curves. From the results obtained, we consider some families of analytic differential systems inℂ2, and imposing the formal integrability we find resonant centers obviating the computation of some necessary conditions.

scholarly journals Blow-up solutions of cubic differential systems

2008 ◽  
Vol 341 (2) ◽  
pp. 1155-1162 ◽  
Author(s):  
J. Baris ◽  
E. Wawiórko
Keyword(s):  
Blow Up ◽  
Differential Systems

On blow-up solutions of nonautonomous quadratic differential systems

2006 ◽  
Vol 42 (3) ◽  
pp. 320-326 ◽  
Author(s):  
J. S. Baris ◽  
P. J. Baris ◽  
B. Ruchlewicz
Keyword(s):  
Quadratic Differential ◽  
Blow Up ◽  
Differential Systems

Blow-up solutions of quadratic differential systems

2008 ◽  
Vol 149 (4) ◽  
pp. 1369-1375 ◽  
Author(s):  
J. Baris ◽  
P. Baris ◽  
B. Ruchlewicz
Keyword(s):  
Quadratic Differential ◽  
Blow Up ◽  
Differential Systems

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System
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