On the existence and multiplicity of eigenvalues for a class of double-phase non-autonomous problems with variable exponent growth
We study the following class of double-phase nonlinear eigenvalue problems − div [φ(x, |∇u|)∇u + ψ(x, |∇u|)∇u] = λ f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain from RN with smooth boundary and the potential functions φ and ψ have (p1(x); p2(x)) variable growth. The main results of this pap...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2020.1.28 |
| Online Access: | http://acta.bibl.u-szeged.hu/69532 |
| Tartalmi kivonat: | We study the following class of double-phase nonlinear eigenvalue problems − div [φ(x, |∇u|)∇u + ψ(x, |∇u|)∇u] = λ f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain from RN with smooth boundary and the potential functions φ and ψ have (p1(x); p2(x)) variable growth. The main results of this paper are to prove the existence of a continuous spectrum consisting in a bounded interval in the near proximity of the origin, the fact that the multiplicity of every eigenvalue located in this interval is at least two and to establish the existence of infinitely many solutions for our problem. The proofs rely on variational arguments based on the Ekeland’s variational principle, the mountain pass theorem, the fountain theorem and energy estimates. |
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| ISSN: | 1417-3875 |