Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach

Drábek, Pavel, Moudan, Zakaria, and Touzani, Abdelfettah. "Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 421-431. <http://eudml.org/doc/248097>.

@article{Drábek1997,
abstract = {The nonlinear eigenvalue problem for p-Laplacian \[ \left\lbrace \begin\{array\}\{ll\}- \operatorname\{div\} (a(x) |\nabla u|^\{p-2\} \nabla u) = \lambda g (x) |u|^\{p-2\} u \text\{ in \} \mathbb \{R\}^N, \ u >0 \text\{ in \} \mathbb \{R\}^N, \mathop \{\lim \}\limits \_\{|x|\rightarrow \infty \} u(x) = 0, \end\{array\}\right.\] is considered. We assume that $1 < p < N$ and that $g$ is indefinite weight function. The existence and $C^\{1, \alpha \}$-regularity of the weak solution is proved.},
author = {Drábek, Pavel, Moudan, Zakaria, Touzani, Abdelfettah},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {eigenvalue; the p-Laplacian; indefinite weight; regularity; -Laplacian; eigenvalue; indefinite weight; regularity},
language = {eng},
number = {3},
pages = {421-431},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach},
url = {http://eudml.org/doc/248097},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Drábek, Pavel
AU - Moudan, Zakaria
AU - Touzani, Abdelfettah
TI - Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 421
EP - 431
AB - The nonlinear eigenvalue problem for p-Laplacian \[ \left\lbrace \begin{array}{ll}- \operatorname{div} (a(x) |\nabla u|^{p-2} \nabla u) = \lambda g (x) |u|^{p-2} u \text{ in } \mathbb {R}^N, \ u >0 \text{ in } \mathbb {R}^N, \mathop {\lim }\limits _{|x|\rightarrow \infty } u(x) = 0, \end{array}\right.\] is considered. We assume that $1 < p < N$ and that $g$ is indefinite weight function. The existence and $C^{1, \alpha }$-regularity of the weak solution is proved.
LA - eng
KW - eigenvalue; the p-Laplacian; indefinite weight; regularity; -Laplacian; eigenvalue; indefinite weight; regularity
UR - http://eudml.org/doc/248097
ER -

References

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Citations in EuDML Documents

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Andrzej Szulkin, Michel Willem, Eigenvalue problems with indefinite weight

NotesEmbed ?

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