Periodic and subharmonic solutions for a class of non-autonomous Hamiltonian systems

Some existence theorems are obtained for periodic and subharmonic solutions of a class of non-autonomous Hamiltonian systems. Our technical approach is based on a version of the Local Linking Theorem, and the Generalized Mountain Pass Theorem.     

On a property of plane curves

Let γ:[0,1]→²[0,1] be a continuous curve such that γ(0)=(0,0), γ(1)=(1,1), and γ(t)∈²(0,1) for all t∈(0,1). We prove that, for each n∈N, there exists a sequence of points Ai, 0?i?n+1, on γ such that A₀=(0,0), An+1=(1,1), and the sequences and , 0?i?n, are positive and the same up to order, where π₁, π₂ are projections on the axes.     

Existence of solutions to nonlinear Hammerstein integral equations and applications

In this paper, we study the existence and multiplicity of solutions of the operator equation Kfu=u in the real Hilbert space L²(G). Under certain conditions on the linear operator K, we establish the conditions on f which are able to guarantee that the operator equation has at least one solution, a unique solution, and infinitely many solutions, respectively. The monotone operator principle and the critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator K1/2 and its properties play an important role. As an application, we investigate the existence and multiplicity of solutions to fourth-order boundary value problems for ordinary differential equations with two parameters, and give some new existence results of solutions.     

Co(Ⅱ)和Ni(Ⅱ)在北山花岗岩上的吸附：表面配位模型及线性自由能关系

用批式法研究了Co(Ⅱ)和Ni(Ⅱ)在北山花岗岩(BS03, 600 m)上的吸附. Co(Ⅱ)和Ni(Ⅱ)在北山花岗岩上的吸附分配比(K_d)均随pH值、离子强度和吸附质浓度的变化而变化; 在低pH值范围, Co(Ⅱ)和Ni(Ⅱ)的K_d 值随离子强度的增大显著减小, 而在高pH值范围,离子强度对K_d的影响较小; Co(Ⅱ)和Ni(Ⅱ)在北山花岗岩上的吸附作用可以分别用1个离子交换反应和2个内层表面配位反应进行定量描述. 建立了表面配位反应平衡常数(K)与过渡金属二价离子水解常数(^OHK)之间的线性自由能关系(LFER),据此对Pb(Ⅱ)和Cu(Ⅱ)在花岗岩上的吸附进行了预测,并与实验结果进行了对比,获得了较好的一致性.     

The one-phase bifurcation for the p-Laplacian

A bifurcation about the uniqueness of a solution of a singularly perturbed free boundary problem of phase transition associated with the p-Laplacian, subject to given boundary condition is proved in this paper. We show this phenomenon by proving the existence of a third solution through the Mountain Pass Lemma when the boundary data decreases below a threshold. In the second part, we prove the convergence of an evolution to stable solutions, and show the Mountain Pass solution is unstable in this sense.     

具有凹凸非线性项和变号位势函数拟线性椭圆系统解的多重结果

研究拟线性椭圆系统(?)的非平凡非负解或正解的多重性,这里Ω(?)R~N是具有光滑边界(?)Ω的有界域,1≤qp~*/p~*-q,其中当N≤p时,p~*=+∞,而当1相似文献   

关于一类带有非线性边界条件的拟线性椭圆方程

本文研究了一类带有非线性边界条件的拟线性椭圆方程.在比常用的经典条件弱的假设条件下,得到该方程所对应的能量泛函存在有界Palais-Smale序列.然后,利用山路引理,得到该方程非平凡解的存在性.最后,给出一个例子,说明所给的条件比经典条件弱.     

Existence of nontrivial solutions of an asymptotically linear fourth-order elliptic equation

In this paper, using the mountain pass theorem, we give the existence result for nontrivial solutions for a class of asymptotically linear fourth-order elliptic equations.     

RN上一类半线性椭圆方程组的多重解

利用对称山路引理,L2(RN)上加权Sobolev空间紧嵌入定理和一个线性耦合特征值问题,本文证明了RN上一类半线性椭圆方程组的多重解的存在性.     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATION WITH CONVEX AND CONCAVE NONLINEARITIES

In this paper, we consider the existence of positive solutions of the semlinear elliptic boundary value problem with convex and concave nonlinearities, the results obtained improve and generalize some known results.