RT Journal Article
T1 A generalization of an extensible beam equation with critical growth in RN
A1 Cabada Fernández, Alberto
A1 Figueiredo, Giovany M.
K1 Beam equation
K1 Critical exponent
K1 Variational methods
AB In this work we obtain an existence  result for a generalized extensible beam equation with critical growth in $\mathbb{R}^{N}$ of the type $$\Delta^{2}u-M\biggl(\dis\int_{\mathbb{R}^{N}}|\nabla u|^{2} \ dx\ \biggl)\Delta u +u = \lambda f(u)+  |u|^{2^{**}-2}u \ \mbox{in} \ \ \mathbb{R}^{N}, $$ where $N\geq 5$ and $\lambda>0$. The functions $M:[0,+\infty)\rightarrow \mathbb{R}$ and $f:\mathbb{R}\rightarrow \mathbb{R}$ are continuous. Since there is a competition between the function $M$ and the critical exponent given by $2^{**}=\frac{2N}{N-4}$, we need to make a truncation on function $M$. Using the size of $\lambda$, we show that each solution of auxiliary problem is a solution of original problem. Our approach is variational  and uses minimax point critical theorems
PB Elsevier
SN 1468-1218
YR 2014
FD 2014-12
LK https://hdl.handle.net/10347/45927
UL https://hdl.handle.net/10347/45927
LA eng
NO Alberto Cabada, Giovany M. Figueiredo, A generalization of an extensible beam equation with critical growth in RN, Nonlinear Analysis: Real World Applications, Volume 20, 2014, Pages 134-142, ISSN 1468-1218, https://doi.org/10.1016/j.nonrwa.2014.05.005. (https://www.sciencedirect.com/science/article/pii/S1468121814000613)
NO First author was supported by FEDER and Ministerio de Educación y Ciencia, Spain, project MTM2010-15314. Second author was supported by PROCAD/CASADINHO: 552101/2011-7, CNPq/PQ 301242/2011-9 and CNPq/CSF 200237/2012-8
DS Minerva
RD 6 jun 2026