Geodesic
Singular problems on the half-line
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 109-128 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half-line of the form \[(p(t)u^{\prime }(t))^{\prime } = p(t)f(u(t)),\] \[u^{\prime }(0) = 0,\quad u(\infty ) = L.\] The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved by the dynamical systems approach and the lower and upper functions method.
The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half-line of the form \[(p(t)u^{\prime }(t))^{\prime } = p(t)f(u(t)),\] \[u^{\prime }(0) = 0,\quad u(\infty ) = L.\] The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved by the dynamical systems approach and the lower and upper functions method.
Classification : 34B16, 34B40
Keywords: Singular ordinary differential equation of the second order; lower and upper functions; time singularities; unbounded domain; homoclinic solution 
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Rachůnková, Irena; Tomeček, Jan. Singular problems on the half-line. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 48 (2009) no. 1, pp. 109-128. http://geodesic.mathdoc.fr/item/AUPO_2009_48_1_a9/

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