In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations disc...In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.展开更多
In this paper, the solvability of singular one dimensional p-Laplacian-like equation with Neumann boundary conditions is considered. Under certain conditions on the operator and the nonlinear term which allows singula...In this paper, the solvability of singular one dimensional p-Laplacian-like equation with Neumann boundary conditions is considered. Under certain conditions on the operator and the nonlinear term which allows singularity, the sufficient and necessary condition for the existence of the solution to the problem is obtained. The main method is based on a-priori estimate for the lower bound of solutions, truncation arguments and the Schauder's fixed point theorem.展开更多
By the use of continuation theorems and the duality principle it＇s proved that for both homogeneous and nonhomogeneous Sturm-Liouville boundary value problems with Laplacian type operators, relative superlinearity im...By the use of continuation theorems and the duality principle it＇s proved that for both homogeneous and nonhomogeneous Sturm-Liouville boundary value problems with Laplacian type operators, relative superlinearity implies the existence of infinitely many solutions under a few weakly added conditions.展开更多
基金Supported by the National Natural Science Foundation of China (No. 10771074)
文摘In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.
基金the Youth Fund of USTC, Thud of Chinese Academy of Sciences and the National Natural Science Foundation of China (No.10071080)
文摘In this paper, the solvability of singular one dimensional p-Laplacian-like equation with Neumann boundary conditions is considered. Under certain conditions on the operator and the nonlinear term which allows singularity, the sufficient and necessary condition for the existence of the solution to the problem is obtained. The main method is based on a-priori estimate for the lower bound of solutions, truncation arguments and the Schauder's fixed point theorem.
基金Supported by Natural Science Foundation of Education Department of Anhui Province (KJ2010B353)Young Teacher’s Foundation of Anhui Normal University (2008xqn46)
基金The project is supported by the National Natural Science Foundation(10371006)
文摘By the use of continuation theorems and the duality principle it＇s proved that for both homogeneous and nonhomogeneous Sturm-Liouville boundary value problems with Laplacian type operators, relative superlinearity implies the existence of infinitely many solutions under a few weakly added conditions.
