摘要
By the Mountain Pass Theorem, we study existence and multiplicity of posi- tive solutions of p-laplacian equation of the form - △pu =λf （x, u）, the nonlinearity f （x, u） grows as u^δ at infinity with a singular coefficient, where a ∈ （p - 1,p＊ - 1）. To manage the asymptotic behavior of its positive solutions with respect to λ, we establish a new Liouville-type theorem for the p-Laplacian operator.
By the Mountain Pass Theorem, we study existence and multiplicity of posi- tive solutions of p-laplacian equation of the form - △pu =λf （x, u）, the nonlinearity f （x, u） grows as u^δ at infinity with a singular coefficient, where a ∈ （p - 1,p＊ - 1）. To manage the asymptotic behavior of its positive solutions with respect to λ, we establish a new Liouville-type theorem for the p-Laplacian operator.
基金
supported by the National Natural Science Foundation of China10771032
