Sign changing solutions for elliptic equations with critical growth in cylinder type domains

Pedro Girão; Miguel Ramos

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 407-419
  • ISSN: 1292-8119

Abstract

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We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, u H 0 1 ( Ω ) , where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of N lying between two infinite cylinders.

How to cite

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Girão, Pedro, and Ramos, Miguel. "Sign changing solutions for elliptic equations with critical growth in cylinder type domains." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 407-419. <http://eudml.org/doc/90628>.

@article{Girão2010,
abstract = { We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, $u\in \{\rm H_0^1\}(\Omega)$, where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of $\mathbb\{R\}^N$ lying between two infinite cylinders. },
author = {Girão, Pedro, Ramos, Miguel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Nodal solutions; cylindrical domains; semilinear elliptic equation; critical Sobolev exponent; con cen tra tion-compactness.; nodal solutions; critical Sobolev exponent; concentration-compactness},
language = {eng},
month = {3},
pages = {407-419},
publisher = {EDP Sciences},
title = {Sign changing solutions for elliptic equations with critical growth in cylinder type domains},
url = {http://eudml.org/doc/90628},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Girão, Pedro
AU - Ramos, Miguel
TI - Sign changing solutions for elliptic equations with critical growth in cylinder type domains
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 407
EP - 419
AB - We prove the existence of positive and of nodal solutions for -Δu = |u|p-2u + µ|u|q-2u, $u\in {\rm H_0^1}(\Omega)$, where µ > 0 and 2 < q < p = 2N(N - 2) , for a class of open subsets Ω of $\mathbb{R}^N$ lying between two infinite cylinders.
LA - eng
KW - Nodal solutions; cylindrical domains; semilinear elliptic equation; critical Sobolev exponent; con cen tra tion-compactness.; nodal solutions; critical Sobolev exponent; concentration-compactness
UR - http://eudml.org/doc/90628
ER -

References

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  9. I. Schindler and K. Tintarev, Abstract concentration compactness and elliptic equations on unbounded domains, in Prog. Nonlinear Differential Equations Appl., Vol. 43, edited by M.R. Grossinho, M. Ramos, C. Rebelo and L. Sanchez. Birkhäuser, Boston (2001) 369-380.  Zbl1030.35080
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