Adams Type Inequality and Application for a Class of Polyharmonic Equations with Critical Growth

作者：do O Joao Marcos^*; Macedo Abiel Costa

来源：Advanced Nonlinear Studies, 2015, 15(4): 867-888.

DOI：10.1515/ans-2015-0407

• Polyharmonic operators
• Trudinger-Moser inequality
• Adams' inequality
• Exponential growth
• Semilinear problems on unbounded domains

In this paper we give a new Adams type inequality for the Sobolev space W-m,W-2(R-2m). By using this inequality in combination with mini- max method we establish the existence of nontrivial solutions to the following class of polyharmonic equations
(-Delta)(m)u(x) + u(x) = f (vertical bar x vertical bar, u), in R-2m,
where the nonlinearity is "superlinear" and has critical exponential growth at infinite.

• 出版日期2015-11