NONLINEAR BIHARMONIC PROBLEMS WITH SINGULAR POTENTIALS

作者：Carriao P C^*; Demarque R; Miyagaki O H

来源：Communications on Pure and Applied Analysis, 2014, 13(6): 2141-2154.

DOI：10.3934/cpaa.2014.13.2141

• Biharmonic operator
• critical potential
• radially symmetric solution

We deal with the problem %26lt;br%26gt;Delta(2)u + V (vertical bar x vertical bar)u - f(u), u is an element of D-2,D-2 (R-N) %26lt;br%26gt;where Delta(2) is biharmonic operator and the potential V %26gt; 0 is measurable, singular at the origin and may also have a continuous set of singularities. The nonlinearity is continuous and has a super-linear power-like behaviour; both sub-critical and super-critical cases are considered. We prove the existence of nontrivial radial solutions. If f is odd, we show that the problem has infinitely many radial solutions.

• 出版日期2014-11