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

Pedro Girão; Miguel Ramos

ESAIM: Control, Optimisation and Calculus of Variations (2002)

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

Abstract

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We prove the existence of positive and of nodal solutions for - Δ u = | u | p - 2 u + μ | u | q - 2 u , u ∈ H 0 1 ( Ω ) , where μ > 0 and 2 < q < p = 2 N ( N - 2 ) , for a class of open subsets Ω of ℝ 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 (2002): 407-419. <http://eudml.org/doc/244857>.

@article{Girão2002,
abstract = {We prove the existence of positive and of nodal solutions for $-\Delta u = |u|^\{p-2\}u+\mu |u|^\{q-2\}u$, $u\in \{\rm H_0^1\}(\Omega )$, where $\mu &gt;0$ and $2&lt; q &lt; p=2N(N-2)$, for a class of open subsets $\Omega $ 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; concentration-compactness},
language = {eng},
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/244857},
volume = {7},
year = {2002},
}

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
PY - 2002
PB - EDP-Sciences
VL - 7
SP - 407
EP - 419
AB - We prove the existence of positive and of nodal solutions for $-\Delta u = |u|^{p-2}u+\mu |u|^{q-2}u$, $u\in {\rm H_0^1}(\Omega )$, where $\mu &gt;0$ and $2&lt; q &lt; p=2N(N-2)$, for a class of open subsets $\Omega $ of $\mathbb {R}^N$ lying between two infinite cylinders.
LA - eng
KW - nodal solutions; cylindrical domains; semilinear elliptic equation; critical Sobolev exponent; concentration-compactness
UR - http://eudml.org/doc/244857
ER -

References

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