We investigate some boundary value problems for an Emden--Fowler type differential system u1′=g1(t)(u2)^{λ},u2′=g2(t)(u1)^{m} on a finite or infinite interval I=[a,b), where gi :I→[0,∞) (i=1,2), are locally integrable functions. We give the optimal, in a certain sense, sufficient conditions which guarantee the existence of a unique (at least of one) nonnegative solution, satisfying one of the two following boundary conditions: i) u1(a)=c, lim u1(t)=d as t tends to b; ii) u2(a)=c,lim u1(t)=d, as t tends to b; in case 0≤c<+∞ (in case c≥0, d=+∞ and λm>1). Moreover, the global two-sided estimations of the above-mentioned solutions are obtained together with applications to differential equations with p-Laplacian.
On nonnegative solutions of singular boundary value problems for Emden-Fowler type differential systems / M. CECCHI;Z. DOSLA;I. KIGURADZE; M. MARINI. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 20:(2007), pp. 1081-1106. [10.57262/die/1356039297]
On nonnegative solutions of singular boundary value problems for Emden-Fowler type differential systems
MARINI, MAURO
2007
Abstract
We investigate some boundary value problems for an Emden--Fowler type differential system u1′=g1(t)(u2)^{λ},u2′=g2(t)(u1)^{m} on a finite or infinite interval I=[a,b), where gi :I→[0,∞) (i=1,2), are locally integrable functions. We give the optimal, in a certain sense, sufficient conditions which guarantee the existence of a unique (at least of one) nonnegative solution, satisfying one of the two following boundary conditions: i) u1(a)=c, lim u1(t)=d as t tends to b; ii) u2(a)=c,lim u1(t)=d, as t tends to b; in case 0≤c<+∞ (in case c≥0, d=+∞ and λm>1). Moreover, the global two-sided estimations of the above-mentioned solutions are obtained together with applications to differential equations with p-Laplacian.File | Dimensione | Formato | |
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