Uniqueness of the Weak Extremal Solution to Biharmonic Equation with Logarithmically Convex Nonlinearities
Year: 2010
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 4 : pp. 315–329
Abstract
In this note, we investigate the existence of the minimal solution and the uniqueness of the weak extremal (probably singular) solution to the biharmonic equation Δ^2ω=λg(ω) with Dirichlet boundary condition in the unit ball in R^n, where the source term is logarithmically convex. An example is also given to illustrate that the logarithmical convexity is not a necessary condition to ensure the uniqueness of the extremal solution.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v23.n4.2
Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 4 : pp. 315–329
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Biharmonic equation
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Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold
Niu, Miaomiao
Tang, Zhongwei
Wang, Lushun
Communications in Contemporary Mathematics, Vol. 20 (2018), Iss. 04 P.1750047
https://doi.org/10.1142/S021919971750047X [Citations: 4]