In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g a...In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.展开更多
In this paper we prove a very general result concerning solvability of the resonant problem: Δu+λ<sub>k</sub>u+g（x, u）=h（x）;u=0, xΩ, which immediately gives three generalized Landesman-Lazer conditi...In this paper we prove a very general result concerning solvability of the resonant problem: Δu+λ<sub>k</sub>u+g（x, u）=h（x）;u=0, xΩ, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when λ<sub>k</sub>=λ<sub>1</sub>. in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.展开更多
In this paper, we give a Landesman-Lazer type theorem for periodic solutions of the asymmetric 1-dimensional p-Laplacian equation -（｜x＇｜^p-2x＇）＇=λ｜x｜^p-2x＋＋μ｜x｜^p-2x-＋f（t,x）with periodic boundary value.
We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of ...We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.展开更多
基金supported by the National Natural Science Foundation of China(No.10325103)the Chinese Scholarship Council(No.201206010092)
文摘In this paper, the authors are concerned with the forced isochronous oscillators with a repulsive singularity and a bounded nonlinearity x'' + V'(x) + g(x) = e(t, x, x'),where the assumptions on V, g and e are regular, described precisely in the introduction.Using a variant of Moser's twist theorem of invariant curves, the authors show the existence of quasi-periodic solutions and boundedness of all solutions. This extends the result of Liu to the case of the above system where e depends on the velocity.
文摘In this paper we prove a very general result concerning solvability of the resonant problem: Δu+λ<sub>k</sub>u+g（x, u）=h（x）;u=0, xΩ, which immediately gives three generalized Landesman-Lazer conditions. The most interesting application of the general result is concerned with the problem when λ<sub>k</sub>=λ<sub>1</sub>. in which case we prove solvability results for it under conditions which are not the standard Landesman-Lazer condition or only partly enjoy it. Furthermore, we propose a new sign condition and give a comprehensive extension of a main result of Figueiredo and Ni.
基金This work is supported by NSFC,RFDP of the Ministry of Education of China the 973 Project of the Ministry of Science and Technology of China
文摘In this paper, we give a Landesman-Lazer type theorem for periodic solutions of the asymmetric 1-dimensional p-Laplacian equation -（｜x＇｜^p-2x＇）＇=λ｜x｜^p-2x＋＋μ｜x｜^p-2x-＋f（t,x）with periodic boundary value.
文摘We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.
