Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations
<p/> <p>This paper investigates the singular differential equation <inline-formula> <graphic file="1687-2770-2009-959636-i1.gif"/></inline-formula>, having a singularity at <inline-formula> <graphic file="1687-2770-2009-959636-i2.gif"/>&l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.boundaryvalueproblems.com/content/2009/959636 |
| _version_ | 1819296162352463872 |
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| author | Rachůnková Irena Tomeček Jan |
| author_facet | Rachůnková Irena Tomeček Jan |
| author_sort | Rachůnková Irena |
| collection | DOAJ |
| description | <p/> <p>This paper investigates the singular differential equation <inline-formula> <graphic file="1687-2770-2009-959636-i1.gif"/></inline-formula>, having a singularity at <inline-formula> <graphic file="1687-2770-2009-959636-i2.gif"/></inline-formula>. The existence of a strictly increasing solution (a homoclinic solution) satisfying <inline-formula> <graphic file="1687-2770-2009-959636-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2009-959636-i4.gif"/></inline-formula> is proved provided that <inline-formula> <graphic file="1687-2770-2009-959636-i5.gif"/></inline-formula> has two zeros and a linear behaviour near <inline-formula> <graphic file="1687-2770-2009-959636-i6.gif"/></inline-formula>.</p> |
| first_indexed | 2024-12-24T04:53:43Z |
| format | Article |
| id | doaj.art-a785607999354e00bb0095297ab61a30 |
| institution | Directory Open Access Journal |
| issn | 1687-2762 1687-2770 |
| language | English |
| last_indexed | 2024-12-24T04:53:43Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-a785607999354e00bb0095297ab61a302022-12-21T17:14:27ZengSpringerOpenBoundary Value Problems1687-27621687-27702009-01-0120091959636Homoclinic Solutions of Singular Nonautonomous Second-Order Differential EquationsRachůnková IrenaTomeček Jan<p/> <p>This paper investigates the singular differential equation <inline-formula> <graphic file="1687-2770-2009-959636-i1.gif"/></inline-formula>, having a singularity at <inline-formula> <graphic file="1687-2770-2009-959636-i2.gif"/></inline-formula>. The existence of a strictly increasing solution (a homoclinic solution) satisfying <inline-formula> <graphic file="1687-2770-2009-959636-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2009-959636-i4.gif"/></inline-formula> is proved provided that <inline-formula> <graphic file="1687-2770-2009-959636-i5.gif"/></inline-formula> has two zeros and a linear behaviour near <inline-formula> <graphic file="1687-2770-2009-959636-i6.gif"/></inline-formula>.</p>http://www.boundaryvalueproblems.com/content/2009/959636 |
| spellingShingle | Rachůnková Irena Tomeček Jan Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations Boundary Value Problems |
| title | Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations |
| title_full | Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations |
| title_fullStr | Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations |
| title_full_unstemmed | Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations |
| title_short | Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations |
| title_sort | homoclinic solutions of singular nonautonomous second order differential equations |
| url | http://www.boundaryvalueproblems.com/content/2009/959636 |
| work_keys_str_mv | AT rach367nkov225irena homoclinicsolutionsofsingularnonautonomoussecondorderdifferentialequations AT tome269ekjan homoclinicsolutionsofsingularnonautonomoussecondorderdifferentialequations |