Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities
Abstract We consider the combined effect of concave–convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions. When α + β < 4 $\alpha+ \beta<4$ , since the concave-convex nonlinearities do not satisfy the mountain pass geo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-02-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02556-6 |
| _version_ | 1818219049922854912 |
|---|---|
| author | Qingjun Lou Yupeng Qin |
| author_facet | Qingjun Lou Yupeng Qin |
| author_sort | Qingjun Lou |
| collection | DOAJ |
| description | Abstract We consider the combined effect of concave–convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions. When α + β < 4 $\alpha+ \beta<4$ , since the concave-convex nonlinearities do not satisfy the mountain pass geometry, it is difficult to obtain a bounded Palais–Smale sequence by the usual mountain pass theorem. To overcome the problem, we properly introduce a method of Nehari manifold and then establish the existence of multiple positive solutions when the pair of the parameters is under a certain range. |
| first_indexed | 2024-12-12T07:33:29Z |
| format | Article |
| id | doaj.art-e6b4a2afa473480a839ac6bb7bc972b0 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T07:33:29Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e6b4a2afa473480a839ac6bb7bc972b02022-12-22T00:32:58ZengSpringerOpenAdvances in Difference Equations1687-18472020-02-012020111310.1186/s13662-020-02556-6Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearitiesQingjun Lou0Yupeng Qin1School of Mathematical Sciences, University of JinanSchool of Science, Henan Institute of TechnologyAbstract We consider the combined effect of concave–convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions. When α + β < 4 $\alpha+ \beta<4$ , since the concave-convex nonlinearities do not satisfy the mountain pass geometry, it is difficult to obtain a bounded Palais–Smale sequence by the usual mountain pass theorem. To overcome the problem, we properly introduce a method of Nehari manifold and then establish the existence of multiple positive solutions when the pair of the parameters is under a certain range.http://link.springer.com/article/10.1186/s13662-020-02556-6Kirchhoff systemMultiple positive solutionsNehari manifold |
| spellingShingle | Qingjun Lou Yupeng Qin Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities Advances in Difference Equations Kirchhoff system Multiple positive solutions Nehari manifold |
| title | Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities |
| title_full | Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities |
| title_fullStr | Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities |
| title_full_unstemmed | Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities |
| title_short | Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave–convex nonlinearities |
| title_sort | existence of multiple positive solutions for a truncated kirchhoff type system involving weight functions and concave convex nonlinearities |
| topic | Kirchhoff system Multiple positive solutions Nehari manifold |
| url | http://link.springer.com/article/10.1186/s13662-020-02556-6 |
| work_keys_str_mv | AT qingjunlou existenceofmultiplepositivesolutionsforatruncatedkirchhofftypesysteminvolvingweightfunctionsandconcaveconvexnonlinearities AT yupengqin existenceofmultiplepositivesolutionsforatruncatedkirchhofftypesysteminvolvingweightfunctionsandconcaveconvexnonlinearities |