Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.
The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN, is studied in this paper. We discuss the corr...The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN, is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone＇s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.展开更多
基金Supported by the National Nature Science Foundation of China( 1037099)
文摘Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.
基金Supported by the National Natural Science Foundation of China (No. 11171220)Shanghai Leading Academic Discipline Project (No. S30501)
文摘The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN, is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone＇s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.
