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.
Communications in Partial Differential Equations
- 10 Reduced Inequalities