Nonlinear initial-value problems with positive global solutions
We give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem {gather*} frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,quadmbox{for }t>0, y(0)=0,quad lim_{t o 0^+} p(t)y'(t) = B, end{gather*} has at least one positive solution for all $t>0$,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/10/b1/abstr.html |
| _version_ | 1811260288963444736 |
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| author | John V. Baxley Cynthia G. Enloe |
| author_facet | John V. Baxley Cynthia G. Enloe |
| author_sort | John V. Baxley |
| collection | DOAJ |
| description | We give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem {gather*} frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,quadmbox{for }t>0, y(0)=0,quad lim_{t o 0^+} p(t)y'(t) = B, end{gather*} has at least one positive solution for all $t>0$, when $B$ is a sufficiently small positive constant. We allow a singularity at $t=0$ so the solution $y'(t)$ may be unbounded near $t=0$. |
| first_indexed | 2024-04-12T18:44:08Z |
| format | Article |
| id | doaj.art-456e171f82b94379a299b26d94375b38 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T18:44:08Z |
| publishDate | 2003-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-456e171f82b94379a299b26d94375b382022-12-22T03:20:39ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-02-01Conference107178Nonlinear initial-value problems with positive global solutionsJohn V. BaxleyCynthia G. EnloeWe give conditions on $m(t)$, $p(t)$, and $f(t,y,z)$ so that the nonlinear initial-value problem {gather*} frac{1}{m(t)} (p(t)y')' + f(t,y,p(t)y') = 0,quadmbox{for }t>0, y(0)=0,quad lim_{t o 0^+} p(t)y'(t) = B, end{gather*} has at least one positive solution for all $t>0$, when $B$ is a sufficiently small positive constant. We allow a singularity at $t=0$ so the solution $y'(t)$ may be unbounded near $t=0$.http://ejde.math.txstate.edu/conf-proc/10/b1/abstr.htmlNonlinear initial-value problemspositive global solutionsCaratheodory. |
| spellingShingle | John V. Baxley Cynthia G. Enloe Nonlinear initial-value problems with positive global solutions Electronic Journal of Differential Equations Nonlinear initial-value problems positive global solutions Caratheodory. |
| title | Nonlinear initial-value problems with positive global solutions |
| title_full | Nonlinear initial-value problems with positive global solutions |
| title_fullStr | Nonlinear initial-value problems with positive global solutions |
| title_full_unstemmed | Nonlinear initial-value problems with positive global solutions |
| title_short | Nonlinear initial-value problems with positive global solutions |
| title_sort | nonlinear initial value problems with positive global solutions |
| topic | Nonlinear initial-value problems positive global solutions Caratheodory. |
| url | http://ejde.math.txstate.edu/conf-proc/10/b1/abstr.html |
| work_keys_str_mv | AT johnvbaxley nonlinearinitialvalueproblemswithpositiveglobalsolutions AT cynthiagenloe nonlinearinitialvalueproblemswithpositiveglobalsolutions |