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Existence of positive solutions for some polyharmonic nonlinear equations in \(\mathbb R^{n}\). (English) Zbl 1136.35370

Summary: We study the polyharmonic nonlinear elliptic equation \((-\Delta)^{m}u+f(\cdot,u)=0\) in \(\mathbb{R}^{n}\), \(n>2m\). 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.

MSC:

35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35A08 Fundamental solutions to PDEs
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