Geodesic
Strongly monotone solutions of systems of nonlinear differential equations with rapidly varying coefficients
Filomat, Tome 36 (2022) no. 18, p. 6317

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DOI

The two-dimensional systems of first order nonlinear differential equations (S 1) x ′ = p(t)y α , y ′ = q(t)x β and (S 2) x ′ + p(t)y α = 0, y ′ + q(t)x β = 0 are analyzed using the theory of rapid variation. This approach allows us to prove that all strongly increasing solutions of system (S 1) (and, respectively, all strongly decreasing solutions of system (S 2)) are rapidly varying functions under the assumption that p and q are rapidly varying. Also, the asymptotic equivalence relations for these solutions are given.
DOI : 10.2298/FIL2218317M
Classification : 34A34, 26A12
Keywords: Systems of nonlinear differential equations, positive solutions, strongly increasing (decreasing) solutions, rapidly varying functions 
Jelena V Manojlović; Jelena S Milošević. Strongly monotone solutions of systems of nonlinear differential equations with rapidly varying coefficients. Filomat, Tome 36 (2022) no. 18, p. 6317 . doi: 10.2298/FIL2218317M
@article{10_2298_FIL2218317M,
     author = {Jelena V Manojlovi\'c and Jelena S Milo\v{s}evi\'c},
     title = {Strongly monotone solutions of systems of nonlinear differential equations with rapidly varying coefficients},
     journal = {Filomat},
     pages = {6317 },
     year = {2022},
     volume = {36},
     number = {18},
     doi = {10.2298/FIL2218317M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218317M/}
}
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