Non-power type perturbation for the critical Hénon problem

Liu, Zhongyuan; Liu, Ziying; Xu, Wenrong

doi:10.1063/5.0106650

Cited by 3 publications

(1 citation statement)

References 32 publications

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“…The nonlinearity fε where ε > 0 has been studied in several works (see for instance [5], [7], [12], [13], [17]). The existence of solutions for (Pε) when ε > 0 is guaranteed by a variational argument developed in [12].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

Fourti,

Ghoudi

2024

Nonlinear Differ. Equ. Appl.

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In this paper, we deal with the boundary value problem −∆u = |u| 4/(n−2) u/[ln(e + |u|)] ε in a bounded smooth domain Ω in R n , n ≥ 3 with homogenous Dirichlet boundary condition. Here ε > 0. Clapp et al. in Journal of Diff. Eq. (Vol 275) built a family of solution blowing up if n ≥ 4 and ε small enough.They conjectured in their paper the existence of sign changing solutions which blow up and blow down at the same point. Here we give a confirmative answer by proving that our slightly subcritical problem has a solution with the shape of sign changing bubbles concentrating on a stable critical point of the Robin function for ε sufficiently small.

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Section: Introduction and Resultsmentioning

confidence: 99%

Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

Fourti,

Ghoudi

2024

Nonlinear Differ. Equ. Appl.

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On a biharmonic elliptic problem with slightly subcritical non-power nonlinearity

Deng,

2023

J. Fixed Point Theory Appl.

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Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

Fourti,

Ghoudi

2023

Preprint

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In this paper, we deal with the boundary value problem -Δu = |u|4/(n-2)u/[ln (e+|u|)]ε in a bounded smoothdomain Ω in ℝn, n ≥ 3 with homogenousDirichlet boundary condition. Here ε > 0. Clapp et al. in Journalof Diff. Eq. (Vol 275) built a family of solution blowing up if n ≥ 4 and ε small enough. They conjectured in their paper the existence of sign changing solutions which blow up and blow down at the same point. Here we give a confirmative answer by proving that our slightly subcritical problem has a solution with the shape of sign changing bubbles concentrating on a stable critical point of the Robin function for ε sufficiently small. Mathematics Subject Classification 2000: 35J20, 35J60.

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Non-power type perturbation for the critical Hénon problem

Cited by 3 publications

References 32 publications

Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

On a biharmonic elliptic problem with slightly subcritical non-power nonlinearity

Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem

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