Existence and convergence of sign-changing solutions for Kirchhoff-type p-Laplacian problems involving critical exponent in RN
We investigate the existence of sign-changing solutions for Kirchhoff-type problems with p-Laplacian involving critical exponent: 1 + b|∇v| p p ∆pv + a(x)|v| p−2 v = |v| p ∗−2 v + λ f(v), x ∈ R N, where b and λ are positive parameters, ∆pv = div(|∇v| p−2∇v), p Np N−p , 1 < p < N, and | · |p is...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | p-Laplace-feladat, Kirchhoff-típusú probléma |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.20 |
| Online Access: | http://acta.bibl.u-szeged.hu/88900 |
| Tartalmi kivonat: | We investigate the existence of sign-changing solutions for Kirchhoff-type problems with p-Laplacian involving critical exponent: 1 + b|∇v| p p ∆pv + a(x)|v| p−2 v = |v| p ∗−2 v + λ f(v), x ∈ R N, where b and λ are positive parameters, ∆pv = div(|∇v| p−2∇v), p Np 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. |
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| Terjedelem/Fizikai jellemzők: | 30 |
| ISSN: | 1417-3875 |