Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN.
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Date
2018
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Abstract
In this work we study the existence and multiplicity of solutions to the following Kirchhofftype
problem with critical nonlinearity in RN
⎧⎨
⎩
−
(
a + b
∫
RN
|∇u|pdx
)
Δpu = μup∗−1 + λf (x, u); x ∈ RN ,
u ∈ D1,p(RN ),
where N ≥ 2p, μ, λ, a, b > 0 and the nonlinearity f (x, u) satisfies certain subcritical
growth conditions. By using topological and variational methods, infinitely many positive
solutions are obtained.
Description
Keywords
Variational methods, p-Laplacian
Citation
MIYAGAKI, O. H.; LEME, L. C. P.; RODRIGUES, B. M. Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN. Computers & Mathematics with Applications, v. 75, n. 9, p. 3201-3212, maio 2018. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0898122118300579>. Acesso em: 16 jun. 2018.