Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with co...Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.展开更多
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new spa...In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new space for nonlinear elliptic partial differential equations with Hardy potential and critical parameter in R2.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant No.10161010)a fund from Fujian Provincial Education Bureau(Grant No.JA02160).
文摘Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
基金Supported by Science and Technology Foundation of Guizhou Province of China under Grant Qiankehe-J-LKM[2012]19
文摘In this paper,a new Hilbert space is defined which is embedded into W01,q(Ω)for 1≤q<2.By using sign-changing critical point theory,we prove the existence of infinitely many sign-changing solutions in this new space for nonlinear elliptic partial differential equations with Hardy potential and critical parameter in R2.
