The critical problem of Kirchhoff type elliptic equations in dimension four

By D. Naimen. 2014

194 citations recorded by the source corpus.

Abstract We study the following Kirchhoff type elliptic problem, (P) { − ( a + b ∫ Ω | ∇ u | 2 d x ) Δ u = λ u q + μ u 3 , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R 4 is a bounded domain with smooth boundary ∂Ω. Moreover, we assume a , λ , μ > 0 , b ≥ 0 and 1 ≤ q 3 . In this paper, we prove the existence of solutions of (P) . Our tools are the variational method and the concentration compactness argument for PS sequences.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/9d82d3c0dcf2c4d49908b886d843d8eaa791916f

Citations in the corpus

• Infinitely many sign-changing solutions for Kirchhoff type problems in R3 (2019, unknown): “[6, 24, 26, 27, 32, 33] and the references therein.”