Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved...Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.展开更多
We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation：where ω 〉 0, a（x） is a continuous function satisfying 0 〈 a（x） 〈 1 for...We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation：where ω 〉 0, a（x） is a continuous function satisfying 0 〈 a（x） 〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.展开更多
In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solution...In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.展开更多
基金This work is supported by the Youth Foundation, NSFC.
文摘In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.
基金Supported by the Youth Foundations of National Education Commuttee the Committee on Science and Technology of Henan Province
文摘Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in a N-ball or an annulus without monotone assumptions on the nonlinear term f.It is also proved that there is no non-radial positive solution.
基金Supported by National Natural Science Foundation of China （Grant No. 10871060）
文摘We study profiles of positive solutions for quasilinear elliptic boundary blow-up problems and Dirichlet problems with the same equation：where ω 〉 0, a（x） is a continuous function satisfying 0 〈 a（x） 〈 1 for x ∈Ω, Ω is a bounded smooth domain in R^N. We will see that the profile of a minimal positive boundary blow-up solution of the equation shares some similarities to the profile of a positive minimizer solution of the equation with homogeneous Dirichlet boundary condition.
基金supported by ARC grant of Australiasupported by National Natural Sciences Foundations of China (10961016 and 10631030)NSF of Jiangxi(2009GZS0011)
文摘In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem{-△Pu=λ｜u｜q-2u＋μ｜u｜ y-2u,x∈Ω,u=0,x∈δΩ to show that problem （1） possesses infinitely many solutions, where 1 〈 p 〈 N, 1 〈 q 〈 P 〈 γ, Ω∩→ R^N is a smooth bounded domain and λ, μ∈ R.
