Nontrivial solutions of modified nonlinear fourth-order elliptic equation in RN
This paper is concerned with the following fourth-order elliptic equation of the form: Δ2u−Δu−uΔ(u2)+u=|u|p−2u,x∈RN,where Δ2u≔Δ(Δu), 4≤N≤6and p∈2,2∗. By making use of the constrained minimization on a special manifold, we prove that the existence of nontrivial solutions of the above problem for any...
| Published in: | Results in Applied Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-02-01
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| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000055 |
| Summary: | This paper is concerned with the following fourth-order elliptic equation of the form: Δ2u−Δu−uΔ(u2)+u=|u|p−2u,x∈RN,where Δ2u≔Δ(Δu), 4≤N≤6and p∈2,2∗. By making use of the constrained minimization on a special manifold, we prove that the existence of nontrivial solutions of the above problem for any p∈2,2∗. Our result can be regarded as a partial extension of some related literature with 4<p<2∗. |
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| ISSN: | 2590-0374 |