Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem
| dc.contributor.author | Malaguti, Luisa | |
| dc.contributor.author | Marcelli, Cristina | |
| dc.date.accessioned | 2021-01-29T14:12:16Z | |
| dc.date.available | 2021-01-29T14:12:16Z | |
| dc.date.issued | 2003-11-28 | |
| dc.description.abstract | In this paper we investigate the boundary eigenvalue problem x'' - β(c, t, x)x' + g(t, x) = 0 x(-∞) = 0, x(+∞) = 1 depending on the real parameter c. We take β continuous and positive and assume that g is bounded and becomes active and positive only when x exceeds a threshold value θ ∈]0, 1[. At the point θ we allow g(t, ·) to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values c for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one c*. In the special case when β reduces to c + h(x) with h continuous, we also give a non-existence result, for any real c. Our methods combine comparison-type arguments, both for the the first and second order dynamics, with a shooting technique. Some applications of the obtained results are included. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Malaguti, L., & Marcelli, C. (2003). Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem. Electronic Journal of Differential Equations, 2003(118), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13169 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Boundary eigenvalue problems | |
| dc.subject | Positive bounded solutions | |
| dc.subject | Shooting method | |
| dc.title | Existence and multiplicity of heteroclinic solutions for a non-autonomous boundary eigenvalue problem | en_US |
| dc.type | Article |