Duan, YueliangZhou, Yinggao2022-06-082022-06-082017-07-19Duan, Y., & Zhou, Y. (2017). Existence of solutions for Kirchhoff type equations with unbounded potential. Electronic Journal of Differential Equations, 2017(184), pp. 1-12.1072-6691https://hdl.handle.net/10877/15877In this article, we study the Kirchhoff type equation (α + λ ∫ℝ3 |∇u|2 + λb ∫ℝ3u2) [-∆u + bu] = K(x)|u|p-1u, in ℝ3, where α, b > 0, p ∈ (2, 5), λ ≥ 0 is a parameter, and K may be an unbounded potential function. By using variational methods, we prove the existence of nontrivial solutions for the above equation. A cut-off functional and some estimates are used to obtain the bounded Palais-Smale sequences.Text12 pages1 file (.pdf)enAttribution 4.0 Internationalcut-off functionalKirchhoff type problemunbounded potentialvariational methodArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.