Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle | Academic Article individual record
abstract

2015, Taylor & Francis Group, LLC. We study classical positive solutions of the biharmonic inequality (Formula presented.) in exterior domains in n where f: (0, )(0, ) is continuous function. We give lower bounds on the growth of f(s) at s=0 and/or s = such that inequality (0.1) has no C4 positive solution in any exterior domain of n. Similar results were obtained by Armstrong and Sirakov for vf(v) using a method which depends only on properties related to the maximum principle. Since the maximum principle does not hold for the biharmonic operator, we adopt a different approach which relies on a new representation formula and an a priori pointwise bound for nonnegative solutions of 2 u0 in a punctured neighborhood of the origin in n.

publication outlet

Communications in Partial Differential Equations

author list (cited authors)
Ghergu, M., & Taliaferro, S. D.
publication date
2015
publisher
keywords
  • 10 Reduced Inequalities
citation count

4

identifier
171173SE
Digital Object Identifier (DOI)
start page
1029
end page
1069
volume
40
issue
6
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