Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity
In this paper, we study Kirchhoff equations with logarithmic nonlinearity: −(a + b R |∇u| 2 )∆u + V(x)u = |u| p−2u ln u 2 , in Ω, u = 0, on ∂Ω, where a, b > 0 are constants, 4 < p < 2 , Ω is a smooth bounded domain of R3 and V : Ω → R. Using constraint variational method, topological degree...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Kirchhoff, Differenciálegyenlet, Logaritmus |
| doi: | 10.14232/ejqtde.2019.1.47 |
| Online Access: | http://acta.bibl.u-szeged.hu/62271 |
| Tartalmi kivonat: | In this paper, we study Kirchhoff equations with logarithmic nonlinearity: −(a + b R |∇u| 2 )∆u + V(x)u = |u| p−2u ln u 2 , in Ω, u = 0, on ∂Ω, where a, b > 0 are constants, 4 < p < 2 , Ω is a smooth bounded domain of R3 and V : Ω → R. Using constraint variational method, topological degree theory and some new energy estimate inequalities, we prove the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. In particular, some new tricks are used to overcome the difficulties that |u| p−2u ln u 2 is sign-changing and satisfies neither the monotonicity condition nor the Ambrosetti–Rabinowitz condition. |
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| Terjedelem/Fizikai jellemzők: | 1-13 |
| ISSN: | 1417-3875 |