Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space
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In this work we study a class of the critical Kirchhoff-type problems in a Hyperbolic space. Because of the Kirchhoff term, the nonlinearity uq becomes concave for 2 < q < 4. This brings difficulties when proving the boundedness of Palais Smale sequences. We overcome this difficulty by using a scaled functional related with a Pohozaev manifold. In addition, we need to overcome singularities on the unit sphere, so that we use variational methods to obtain our results.
CitationCarrião, P. C., Costa, A. C. D. R., Miyagaki, O. H., & Vicente, A. (2021). Kirchhoff-type problems with critical Sobolev exponent in a hyperbolic space. Electronic Journal of Differential Equations, 2021(53), pp. 1-12.
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