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Volume 25, Issue 4
Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation

Rabeh Ghoudi

DOI: 10.4208/jpde.v25.n4.5

J. Part. Diff. Eq., 25 (2012), pp. 366-386.

Published online: 2012-12

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  • Abstract

This paper is concerned with the following non linear elliptic problem involving nearly critical exponent (P^k_ε): (-Δ)^ku=K(x)|u|^{(4k/(n-1k))-ε}u in Ω, Δ^{k-1}u=…=Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in R^n, n≥ 2k+2, k≥ 1, ε is a small positive parameter and K is a smooth positive function in Ω. We construct signchanging solutions of (P^k_ε) having two bubbles and blowing up either at two different critical points of K with the same speed or at the same critical point.

  • Keywords

Blow-up analysis sign-changing solutions critical exponent

  • AMS Subject Headings

35J20, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ghoudi.rabeh@yahoo.fr (Rabeh Ghoudi)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-366, author = {Ghoudi , Rabeh}, title = {Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {4}, pages = {366--386}, abstract = {

This paper is concerned with the following non linear elliptic problem involving nearly critical exponent (P^k_ε): (-Δ)^ku=K(x)|u|^{(4k/(n-1k))-ε}u in Ω, Δ^{k-1}u=…=Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in R^n, n≥ 2k+2, k≥ 1, ε is a small positive parameter and K is a smooth positive function in Ω. We construct signchanging solutions of (P^k_ε) having two bubbles and blowing up either at two different critical points of K with the same speed or at the same critical point.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n4.5}, url = {http://global-sci.org/intro/article_detail/jpde/5192.html} }
TY - JOUR T1 - Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation AU - Ghoudi , Rabeh JO - Journal of Partial Differential Equations VL - 4 SP - 366 EP - 386 PY - 2012 DA - 2012/12 SN - 25 DO - http://doi.org/10.4208/jpde.v25.n4.5 UR - https://global-sci.org/intro/article_detail/jpde/5192.html KW - Blow-up analysis KW - sign-changing solutions KW - critical exponent AB -

This paper is concerned with the following non linear elliptic problem involving nearly critical exponent (P^k_ε): (-Δ)^ku=K(x)|u|^{(4k/(n-1k))-ε}u in Ω, Δ^{k-1}u=…=Δu=u=0 on ∂Ω, where Ω is a bounded smooth domain in R^n, n≥ 2k+2, k≥ 1, ε is a small positive parameter and K is a smooth positive function in Ω. We construct signchanging solutions of (P^k_ε) having two bubbles and blowing up either at two different critical points of K with the same speed or at the same critical point.

Rabeh Ghoudi. (2020). Blowing Up of Sign-changing Solutions to an Elliptic Subcritical Equation. Journal of Partial Differential Equations. 25 (4). 366-386. doi:10.4208/jpde.v25.n4.5
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