Multiple solutions for a class of Kirchhoff-type equation with critical growth
In this paper, we study the multiplicity of solutions to a class of Kirchhofftype equation with critical growth a + b Z R3 |∇u| 2 dx� ∆u + V(x)u = λh(x)f(u) + g(x)u 5 in R 3 where a, b > 0, λ is a positive parameter and f is a continuous nonlinearity with subcritical growth. Under suitable condit...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Kirchhoff-típusú egyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.7 |
| Online Access: | http://acta.bibl.u-szeged.hu/88887 |
| Tartalmi kivonat: | In this paper, we study the multiplicity of solutions to a class of Kirchhofftype equation with critical growth a + b Z R3 |∇u| 2 dx� ∆u + V(x)u = λh(x)f(u) + g(x)u 5 in R 3 where a, b > 0, λ is a positive parameter and f is a continuous nonlinearity with subcritical growth. Under suitable conditions on the potentials V(x), h(x) and g(x), we prove the multiplicity results and investigate the relation between the number of solutions with the topology of the set where g attains its maximum value for small values of the parameter λ. The proofs are based on Nehari manifold and Lusternik– Schnirelmann theory. |
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| Terjedelem/Fizikai jellemzők: | 25 |
| ISSN: | 1417-3875 |