On the solvability of a higher-order semilinear ODE
The existence of at least one or two nontrivial solutions to a general higher-order boundary value problem is established by using variational tools. Two of the results are obtained without any asymptotic behaviour at infinity of potential $F$ of the nonlinear term $f$, which is a key condition i...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-10-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10935 |
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| _version_ | 1841533490631278592 |
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| author | Cristian-Paul Danet |
| author_facet | Cristian-Paul Danet |
| author_sort | Cristian-Paul Danet |
| collection | DOAJ |
| description | The existence of at least one or two nontrivial solutions to a general higher-order boundary value problem is established by using variational tools. Two of the results are obtained without any asymptotic behaviour at infinity of potential $F$ of the nonlinear term $f$, which is a key condition in the available literature, when applying critical point theorems. Moreover, $F$ may change sign. The last result is stated when the nonlinearity has asymptotic behaviour at both infinity and zero. |
| format | Article |
| id | doaj-art-783c4bad7140421196416d6bd8872680 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-783c4bad7140421196416d6bd88726802025-01-15T21:24:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-10-0120245711710.14232/ejqtde.2024.1.5710935On the solvability of a higher-order semilinear ODECristian-Paul Danet0University of Craiova, Craiova, RomaniaThe existence of at least one or two nontrivial solutions to a general higher-order boundary value problem is established by using variational tools. Two of the results are obtained without any asymptotic behaviour at infinity of potential $F$ of the nonlinear term $f$, which is a key condition in the available literature, when applying critical point theorems. Moreover, $F$ may change sign. The last result is stated when the nonlinearity has asymptotic behaviour at both infinity and zero.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10935odehigher-ordersemilinearbrézis–nirenberg's linking theoremmountain pass theoremvariational method |
| spellingShingle | Cristian-Paul Danet On the solvability of a higher-order semilinear ODE Electronic Journal of Qualitative Theory of Differential Equations ode higher-order semilinear brézis–nirenberg's linking theorem mountain pass theorem variational method |
| title | On the solvability of a higher-order semilinear ODE |
| title_full | On the solvability of a higher-order semilinear ODE |
| title_fullStr | On the solvability of a higher-order semilinear ODE |
| title_full_unstemmed | On the solvability of a higher-order semilinear ODE |
| title_short | On the solvability of a higher-order semilinear ODE |
| title_sort | on the solvability of a higher order semilinear ode |
| topic | ode higher-order semilinear brézis–nirenberg's linking theorem mountain pass theorem variational method |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10935 |
| work_keys_str_mv | AT cristianpauldanet onthesolvabilityofahigherordersemilinearode |