For a Gelfand type semilinear elliptic equation we extend some known results for the Dirichlet problem to the Steklov problem. This extension requires some new tools, such as non-optimal Hardy inequalities, and discovers some new phenomena, in particular a different behavior of the branch of solutions and three kinds of blow-up for large solutions in critical growth equations. We also show that small values of the boundary parameter play against strong growth of the nonlinear source.
@article{AIHPC_2010__27_1_315_0, author = {Berchio, Elvise and Gazzola, Filippo and Pierotti, Dario}, title = {Gelfand type elliptic problems under {Steklov} boundary conditions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {315--335}, publisher = {Elsevier}, volume = {27}, number = {1}, year = {2010}, doi = {10.1016/j.anihpc.2009.09.011}, mrnumber = {2580512}, zbl = {1184.35132}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/} }
TY - JOUR AU - Berchio, Elvise AU - Gazzola, Filippo AU - Pierotti, Dario TI - Gelfand type elliptic problems under Steklov boundary conditions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 315 EP - 335 VL - 27 IS - 1 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/ DO - 10.1016/j.anihpc.2009.09.011 LA - en ID - AIHPC_2010__27_1_315_0 ER -
%0 Journal Article %A Berchio, Elvise %A Gazzola, Filippo %A Pierotti, Dario %T Gelfand type elliptic problems under Steklov boundary conditions %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 315-335 %V 27 %N 1 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/ %R 10.1016/j.anihpc.2009.09.011 %G en %F AIHPC_2010__27_1_315_0
Berchio, Elvise; Gazzola, Filippo; Pierotti, Dario. Gelfand type elliptic problems under Steklov boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 1, pp. 315-335. doi : 10.1016/j.anihpc.2009.09.011. http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.011/
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