非线性四阶周期边值问题正解的存在性和多重性

研究了四阶两参数常微分方程周期边值问题{u（4）（t）-βu″（t）＋αu（t）=f（t,u（τ（t）））,t∈[0,1],u（i）（0）=u（i）（1）,i=1,2,3正解的存在性、多重性和不存在性.在非线性项f（t,u）变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问...     

A boundary value problem associated to non-homogeneous operators in Orlicz-Sobolev spaces

We apply a three critical points theorem of B. Ricceri to establish the existence of at least three weak solutions for a class of non-homogeneous Neumann problems. Furthermore, by using another theorem of him, we prove that an appropriate oscillating behaviour of the nonlinear term ensures the existence of infinitely many weak solutions. Our analysis is based on recent variational methods for smooth functionals defined on Orlicz-Sobolev spaces.     

Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).     

TRIPLE POSITIVE SOLUTIONS OF A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEM

In this paper, we establish an existence criterion of triple positive solutions of a class of nonlinear fourth-order three-point boundary value problem by the LeggettWilliams fixed point theorem. The interesting point is that the nonlinear term is involved with all low-level derivatives.     

Existence of Positive Solutions to Fourth Order Quasilinear Boundary Value Problems

In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some fourth-order beam equation boundary value problems is obtained. The emphasis is put on that the nonlinear term is dependent on all lower order derivatives.     

Nonmonotone, nonlinear evolution inclusions

In this paper, we consider nonlinear evolution problems, defined on an evolution triple of spaces, driven by a nonmonotone operator, and with a perturbation term which is multivalued. We prove existence theorems for the cases of a convex and of a nonconvex valued perturbation term which is defined on all of T × H or only on T × X with values in H or even in X^* (here X - H - X^* is the evolution triple). Also, we prove the existence of extremal solutions, and for the “monotone” problem we have a strong relaxation theorem. Some examples of nonlinear parabolic problems are presented.     

Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential

We consider a nonlinear elliptic problem driven by a nonlinear nonhomogeneous differential operator and a nonsmooth potential. We prove two multiplicity theorems for problems with coercive energy functional. In both theorems we produce three nontrivial smooth solutions. In the second multiplicity theorem, we provide precise sign information for all three solutions (the first positive, the second negative and the third nodal). Out approach is variational, based on the nonsmooth critical point theory. We also prove an auxiliary result relating smooth and Sobolev local minimizer for a large class of locally Lipschitz functionals.     

Existence of positive pseudo almost periodic solutions to a class of neutral integral equations

In this work, a new fixed point theorem in partially ordered Banach spaces is established, and then used to prove the existence of positive pseudo almost periodic solutions to a class of neutral integral equations. Our existence theorem extends some recent results due to [E. Ait Dads, P. Cieutat, L. Lhachimi, Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations, Mathematical and Computer Modelling 49 (2009) 721–739] to a more general class of integral equations.     

具有单调递增同胚和正同态算子二阶三点边值问题三个正解的存在性

利用Leggett-Williams不动点定理研究了一类具有单调递增同胚和正同态算子的边值问题,得到了三个正解存在的一组充分条件.     

Triple positive solutions for boundary value problems on infinite intervals

This paper deals with the existence of triple positive solutions for Sturm–Liouville boundary value problems of second-order nonlinear differential equation on a half line. By using a fixed point theorem in a cone due to Avery–Peterson, we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term.