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Ordinary p ‐Biharmonic Problems
Author(s) -
Benedikt Jiří
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810089
Subject(s) - biharmonic equation , bifurcation , eigenvalues and eigenvectors , mathematics , boundary value problem , operator (biology) , ordinary differential equation , dimension (graph theory) , order (exchange) , laplace operator , differential operator , mathematical analysis , partial differential equation , pure mathematics , differential equation , physics , chemistry , economics , biochemistry , finance , repressor , nonlinear system , quantum mechanics , transcription factor , gene
The aim of this paper is to recall known results on boundary value problems for the quasilinear fourth order differential equation in one dimension 1$$(| u^{\prime\prime}\vert^{p-2}u^{\prime\prime})^{\prime\prime}=f(t,u),\quad t\in[0,1],$$ where p >1. The operator at the left‐hand side is often called a p ‐biharmonic operator which reduces to u (4) for p = 2. It is a fourth order analogue of the well‐known p ‐Laplacian. We discuss spectral properties of the corresponding eigenvalue problems, and existence and global bifurcation of solutions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)