Periodic solutions of angiogenesis models with time lags
To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous s...
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2012
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| 008 | 190411s2012 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-80052813029 | |
| 040 | |a Scopus |b spa |c AR-BaUEN |d AR-BaUEN | ||
| 100 | 1 | |a Amster, P. | |
| 245 | 1 | 0 | |a Periodic solutions of angiogenesis models with time lags |
| 260 | |c 2012 | ||
| 270 | 1 | 0 | |m Amster, P.; Universidad de Buenos Aires, Departamento de Matemática, Ciudad Universitaria - Pab. I, 1428 - Buenos Aires, Argentina; email: pamster@dm.uba.ar |
| 506 | |2 openaire |e Política editorial | ||
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| 504 | |a Mawhin, J., (1979) Topological Degree Methods in Nonlinear Boundary Value Problems, 40. , CBMS Regional Conference Series in Mathematics Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 915, 1977 American Mathematical Society Providence, RI | ||
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| 520 | 3 | |a To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Numerical examples illustrate our findings. Some open problems are presented for further studies. © 2011 Elsevier Ltd. All rights reserved. |l eng | |
| 593 | |a Universidad de Buenos Aires, Departamento de Matemática, Ciudad Universitaria - Pab. I, 1428 - Buenos Aires, Argentina | ||
| 593 | |a Department of Mathematics, Ben-Gurion University of Negev, Beer-Sheva 84105, Israel | ||
| 593 | |a Department of Mathematics, Vancouver Island University, 900 Fifth St., Nanaimo, BC, V9S5S5, Canada | ||
| 690 | 1 | 0 | |a A PRIORI ESTIMATES |
| 690 | 1 | 0 | |a ANGIOGENESIS |
| 690 | 1 | 0 | |a EXISTENCE OF POSITIVE PERIODIC SOLUTIONS |
| 690 | 1 | 0 | |a LERAYSCHAUDER DEGREE METHODS |
| 690 | 1 | 0 | |a NONLINEAR NONAUTONOMOUS DELAY DIFFERENTIAL EQUATIONS |
| 690 | 1 | 0 | |a SECOND ORDER LIENARD TYPE EQUATION |
| 690 | 1 | 0 | |a A-PRIORI ESTIMATES |
| 690 | 1 | 0 | |a ANGIOGENESIS |
| 690 | 1 | 0 | |a EXISTENCE OF POSITIVE PERIODIC SOLUTIONS |
| 690 | 1 | 0 | |a LERAYSCHAUDER DEGREE METHODS |
| 690 | 1 | 0 | |a NONAUTONOMOUS |
| 690 | 1 | 0 | |a SECOND ORDERS |
| 690 | 1 | 0 | |a DIFFERENTIAL EQUATIONS |
| 690 | 1 | 0 | |a DIFFERENTIATION (CALCULUS) |
| 690 | 1 | 0 | |a MATHEMATICAL MODELS |
| 690 | 1 | 0 | |a NONLINEAR EQUATIONS |
| 690 | 1 | 0 | |a PROBLEM SOLVING |
| 700 | 1 | |a Berezansky, L. | |
| 700 | 1 | |a Idels, L. | |
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