Abstract:
In this paper, by using variational methods and critical point theory, we shall mainly study the existence of infinitely many solutions for the following fractional Schr\"odinger-Maxwell equations $$( -\Delta )^{\alpha} u+V(x)u+\phi u=f(x,u), \hbox{in } \mathbb{R}^3 ,$$ $$ (-\triangle)^{\alpha}\phi =K_{\alpha} u^2 \ \ \mathrm{in}\ \ \mathbb{R}^3 $$ where $\alpha \in (0,1],$ $K_{\alpha}=\dfrac{\pi^{-\alpha}\Gamma(\alpha)}{\pi^{-(3-2\alpha)/2}\Gamma((3-2\alpha)/2)},$ $( -\Delta )^{\alpha}$ stands for the fractional Laplacian. Under some more assumptions on $f,$ we get infinitely many solutions for the system.

Abstract:
This article discusses the existence of positive solutions for systems of bending elastic beam equations. In mechanics, the problem describes the deformations of two elastic beams in equilibrium state, whose two ends are simply supported.

Abstract:
In this paper, we study a generalized Sturm-Liouville boundary-value problems with two positive parameters. By constructing a completely continuous operator and combining fixed point index theorem and some properties of the eigenvalues of linear operators, we obtain sufficient conditions for the existence of at least one positive solution.

Abstract:
We study the existence of multiple positive solutions for nth-order multipoint boundary value problem. u(n)(t)+a(t)f(u(t))=0, t∈(0,1), u(j-1)(0)=0(j=1,2,…,n-1), u(1)=∑i=1mαiu(ηi), where n≥2, 0<η1<η2< <ηm<1, αi>0,i=1,2,…,m. We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.

Abstract:
We study the existence of multiple positive solutions for th-order multipoint boundary value problem. , , , , where , , . We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.

Abstract:
This work presents sufficient conditions for the existence and uniqueness of positive solutions for a discrete fourth-order beam equation under Lidstone boundary conditions with a parameter; the iterative sequences yielding approximate solutions are also given. The main tool used is monotone iterative technique.

Abstract:
This work presents sufficient conditions for the existence and uniqueness of positive solutions for a discrete fourth-order beam equation under Lidstone boundary conditions with a parameter; the iterative sequences yielding approximate solutions are also given. The main tool used is monotone iterative technique.

Abstract:
This paper investigates the existence of positive solutions for second-order singular sub-linear three-point boundary value problems. A necessary and sufficient condition for the existence of C 0,1] as well as C10,1] positive solutions is given by constructing lower and upper solutions and with the comparison theorem. The nonlinearity f(t,x) may be singular at , \ t=0 and /or t=1 .

Abstract:
In this paper, we investigate the periodic boundary value problems for firstorder nonlinear impulsive integro-differential equations of mixed type in a Banach space. Byestablishing a new comparison result, criteria on the existence of maximal and minimal solutionsare obtained. The results of the paper essentially improve and supplement recent results givenin 7].

Abstract:
We study the existence of positive solutions for the nonlinear four-point singular boundary-value problem with $p$-Laplacian operator on time scales. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary-value problem with $p$-Laplacian operator are obtained.