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February, 2020 Ground State Solutions for Kirchhoff-type Problems with Critical Nonlinearity
Yiwei Ye
Taiwanese J. Math. 24(1): 63-79 (February, 2020). DOI: 10.11650/tjm/190402

Abstract

In this paper, we study the Kirchhoff-type equation with critical exponent \[ -\left( a + b \int_{\mathbb{R}^3} |\nabla u|^2 \, dx \right) \Delta u + V(x)u = a(x) f(u) + u^5 \quad \textrm{in $\mathbb{R}^3$}, \] where $a,b \gt 0$ are constants, $V \in C(\mathbb{R}^3,\mathbb{R})$, $\lim_{|x| \to \infty} V(x) = V_{\infty} \gt 0$ and $V(x) \leq V_{\infty} + C_1 e^{-b |x|}$ for some $C_1 \gt 0$ and $|x|$ large enough. Via variational methods, we prove the existence of ground state solution.

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Yiwei Ye. "Ground State Solutions for Kirchhoff-type Problems with Critical Nonlinearity." Taiwanese J. Math. 24 (1) 63 - 79, February, 2020. https://doi.org/10.11650/tjm/190402

Information

Received: 2 August 2017; Accepted: 6 March 2019; Published: February, 2020
First available in Project Euclid: 15 April 2019

zbMATH: 07175540
MathSciNet: MR4053838
Digital Object Identifier: 10.11650/tjm/190402

Subjects:
Primary: 45M20
Secondary: 35B33

Keywords: ground state solutions , Kirchhoff-type equation , variational methods

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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