Oscillatory radial solutions for subcritical biharmonic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:247

Article

Lazzo, M.²  Schmidt, P. G.¹ 

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[2] Univ Bari, Dipartimento Matemat, I-70125 Bari, Italy

关键词: Biharmonic equation;    Radial solutions;    Entire solutions;    Large solutions;    Oscillatory behavior;    Dirichlet problem;   

DOI  :  10.1016/j.jde.2009.05.005

来源: Elsevier

【 摘 要 】

It is well known that the biharmonic equation Delta(2)u = u vertical bar u vertical bar(p-1) with P is an element of (1, infinity) has positive solutions on R-n if and only if the growth of the nonlinearity is critical or supercritical. We close a gap in the existing literature by proving the existence and uniqueness, up to scaling and symmetry, of oscillatory radial solutions on R-n in the subcritical case. Analyzing the nodal properties of these solutions, we also obtain precise information about sign-changing large radial solutions and radial solutions of the Dirichlet problem on a ball. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free