Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle

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.

authors

• Taliaferro, Steven

published proceedings

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

author list (cited authors)

• Ghergu, M., & Taliaferro, S. D.

citation count

• 4

complete list of authors

• Ghergu, Marius||Taliaferro, Steven D

publication date

• June 2015

publisher

• Taylor & Francis  Publisher

published in

• COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS  Journal

keywords

• 35a01
• 35b09
• 35b33
• 35j91
• 35r45
• Biharmonic Equation
• Critical Exponent
• Nonexistence
• Supersolution

Digital Object Identifier (DOI)

• 10.1080/03605302.2015.1008364

start page

• 1029

end page

• 1069

volume

• 40

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F03605302.2015.1008364

user-defined tag

• 10 Reduced Inequalities