Existence of positive solutions for some polyharmonic nonlinear equations in ℝ n (Abstract and Applied Analysis)
We will study the following polyharmonic nonlinear elliptic equation ( − ∆ ) m u + f ( ‧ , u ) = 0 in ℝ n , 2m$"> n > 2 m . Under appropriate conditions on the nonlinearity f ( x , t ) , related to a class of functions called m -Green-tight functions, we give some existence results for the above equation.