Extremal solutions to a system of n nonlinear differential equations and regularly varying functions |
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Authors: | Serena Matucci Pavel ?ehák |
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Institution: | 1. Department of Mathematics and Informatics “U. Dini”, University of Florence, Florence, Italy;2. +420 3. 532 4. 290 5. 444+420 6. 541 7. 218 8. 657;9. Institute of Mathematics, Academy of Sciences CR, Czech Republic;10. Faculty of Education, Masaryk University, Czech Republic |
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Abstract: | The strongly increasing and strongly decreasing solutions to a system of n nonlinear first order equations are here studied, under the assumption that both the coefficients and the nonlinearities are regularly varying functions. We establish conditions under which such solutions exist and are (all) regularly varying functions, we derive their index of regular variation and establish asymptotic representations. Several applications of the main results are given, involving n‐th order nonlinear differential equations, equations with a generalized ?‐Laplacian, and nonlinear partial differential systems. |
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Keywords: | Positive extremal solutions asymptotic representation quasilinear systems Emden‐Fowler systems elliptic systems regular variation 34C11 34C41 34Exx 35Jxx |
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