Multispike Solutions for a slightly subcritical elliptic problem with non-power nonlinearity

Ayed, Mohamed Ben; Fourti, Habib; Ghoudi, Rabeh

doi:10.3934/dcds.2022165

Cited by 5 publications

(16 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ε > 0. As mentioned in [7] and [5], there is an interesting analogy between results obtained for (Pε) and those known for the usual elliptic equation (1.9). In this direction, we prove here that (Pε) shares also with problem (1.9), the existence of tower bubbles solutions of different blow-up orders, as conjectured in [7].…”

Section: Introduction and Resultssupporting

confidence: 64%

“…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%

“…In [17], the asymptotic behavior of radially symmetric solutions of (Pε) was analyzed when Ω is a ball. Very recently, we provided in [5] the existence of positive as well as changing sign solutions that blow up and/or blow down at different points in Ω. Our solutions have the following expansion uε = k i=1 αi,εγiP δ (a i,ε ,λ i,ε ) + v where γi ∈ {−1, 1} for each 1 ≤ i ≤ k, αi,ε → 1 λi,ε → ∞, vε ∈ E (a,λ) and vε → 0 as ε goes to 0.…”

Section: Introduction and Resultsmentioning

confidence: 99%

See 2 more Smart Citations

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

Fourti,

Ghoudi

2024

Nonlinear Differ. Equ. Appl.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introduction and Resultssupporting

confidence: 64%

Section: Introduction and Resultsmentioning

confidence: 99%

Section: Introduction and Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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

Fourti,

Ghoudi

2024

Nonlinear Differ. Equ. Appl.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Furthermore, the following integral is needed in the proof of Proposition 2.2 and it was computed in [5]. We have…”

Section: The Technical Frameworkmentioning

confidence: 99%

“…The first one concerns the nonlinearity fε and its derivatives. It is contained in [7] and [5]. (1 + r 2 ) (n+2)/2 ≤ cλ (n−2)/2 ≤ cδ (a,λ) (y).…”

Section: Appendixmentioning

confidence: 99%

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

Fourti,

Ghoudi

2023

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Single‐peak solution for a fractional slightly subcritical problem with non‐power nonlinearity

Deng,

2024

Mathematische Nachrichten

View full text Add to dashboard Cite

We consider the following fractional problem involving slightly subcritical non‐power nonlinearity, where is a smooth bounded domain in , , , is the fractional critical Sobolev exponent and is a small parameter, is the spectral fractional Laplacian operator. We construct a positive bubbling solution, which concentrates at a nondegenerate critical point of the Robin function by Lyapunov–Schmidt reduction procedure.

show abstract

Multispike Solutions for a slightly subcritical elliptic problem with non-power nonlinearity

Cited by 5 publications

References 13 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

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

Single‐peak solution for a fractional slightly subcritical problem with non‐power nonlinearity

Contact Info

Product

Resources

About