On solutions of second and fourth order elliptic equations with power-type nonlinearities

By A. Ferrero, G. Warnault. 2009

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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “S%/ and 2 ! N ! 7? In other words, does one have uniqueness for small !, exactly two solutions for ! close to !!, and a second bifurcation point leading to a quenching branch of solutions? # What can be said in the case of a more general domain? More results on general fourth-order nonlinear eigenva”
On a p(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{p(x)}$$\end{document}-biharmonic problem with singula (2017, background): “We also point out that fourth-order elliptic equations arise in many domains like microelectromechanical systems, surface diffusion on solids, thin film theory, flow in Hele-Shaw cells and phase field models of multiphasic systems (see [13]).”
Multiplicity of solutions for a fourth order equation with power-type nonlinearity (2010, background): “In fact, in [16] the authors show that when N = 3 and p ≤ −1/2 then u∗ is regular.”