Existence and convergence of sign-changing solutions for Kirchhoff-type p -Laplacian problems involving critical exponent in R N

• Published in: Electronic journal of qualitative theory of differential equations no. 20; pp. 1 - 30
• Main Authors: Chahma, Youssouf, Han, Yang
• Format: Journal Article
• Language: English
• Published: 2025
• ISSN: 1417-3875; 1417-3875
• DOI: 10.14232/ejqtde.2025.1.20

We investigate the existence of sign-changing solutions for Kirchhoff-type problems with p -Laplacian involving critical exponent: − ( 1 + b | ∇ v | p p ) Δ p v + a ( x ) | v | p − 2 v = | v | p ∗ − 2 v + λ f ( v ) , x ∈ R N , where b and λ are positive parameters, Δ p v = div ⁡ ( | ∇ v | p − 2 ∇ v ) , p ∗ = N p N − p , 1 < p < N , and | ⋅ | p is the Lebesgue L p -norm. For sufficiently large λ , employing minimization techniques, quantitative deformation lemma and the constrained variational method, we demonstrate the existence of a least-energy sign-changing solution, whose energy is greater than twice that of the ground state solution. Additionally, we show the convergence behavior of the solution as the parameter b ↘ 0 . Our findings generalize and extend upon recent results in the literature.