Normalized solutions for Kirchhoff type equations with combined nonlinearities: The Sobolev critical case
نویسندگان
چکیده
In this paper, we study the Kirchhoff equation with Sobolev critical exponent \begin{document}$ -\left(a+b\int_{ {\mathbb{R}}^3}|\nabla u|^2\right)\Delta u = \lambda u+\mu|u|^{q-2}u+|u|^{4}u\ \ {\rm in}\ {\mathbb{R}}^3 $\end{document} under normalized constraint$ \int_{ {\mathbb{R}}^3}u^2 c^2, $where a, \, b, c>0 are constants, \lambda, \mu\in{\mathbb{R}} and 2<q<6 $\end{document}. The number 2+8/3 behaves as L^2 $\end{document}-critical for above problem. When \mu>0 $\end{document}, distinguish problem into four cases: 2<q<2+4/3 q 2+4/3 2+4/3<q<2+8/3 2+8/3\leq q<6 prove existence multiplicity of solutions suitable assumptions on \mu c solution obtained is either a minimum (local or global) mountain pass solution. \mu\leq 0 establish nonexistence nonnegative solutions. Finally, investigate asymptotic behavior \mu\to0^+ b\to0^+ respectively.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2023
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2023035