The paper deals with the boundary value problem (on the whole line) u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g is a continuous non-negative function with support [0, 1], and f is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for the problem when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u, u'). Applications of these results in the field of front-type solutions for reaction diffusion equations can be found in L. Malaguti, C. Marcelli, Math. Nachr. 242 (2002), 148—164

Existence of Bounded Trajectories Via Upper and Lower Solutions / Malaguti, Luisa; C., Marcelli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 6:(2000), pp. 575-590.

Existence of Bounded Trajectories Via Upper and Lower Solutions

MALAGUTI, Luisa;
2000

Abstract

The paper deals with the boundary value problem (on the whole line) u''-f(u,u')+g(u)=0, u(-∞)=0, u(+∞)=1, where g is a continuous non-negative function with support [0, 1], and f is a continuous function. By means of a new approach, based on a combination of lower and upper-solutions methods and phase-plane techniques, we prove an existence result for the problem when f is superlinear in u'; by a similar technique, we also get a non-existence one. As an application, we investigate the attractivity of the singular point (0,0) in the phase-plane (u, u'). Applications of these results in the field of front-type solutions for reaction diffusion equations can be found in L. Malaguti, C. Marcelli, Math. Nachr. 242 (2002), 148—164
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575
590
Existence of Bounded Trajectories Via Upper and Lower Solutions / Malaguti, Luisa; C., Marcelli. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 6:(2000), pp. 575-590.
Malaguti, Luisa; C., Marcelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/305188
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