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 |
| Summary: | 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. |
|---|---|
| ISSN: | 1687-1847 |