In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. Under different combinations of superlinearity and sublinearity of the nonlinearities, various existence results for positive solutions are derived in terms of different values of parameters via the Guo-Krasnosel'skii fixed point theorem.

In this paper, we study the nonlocal fractional differential equation:continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.

In this paper we study a class of operator equations A(x, x) + B(x, x) = x in ordered Banach spaces, where A, B are two mixed monotone operators. Various theorems are established to guarantee the existence of a unique solution to the problem. In addition, associated iterative schemes have been established for finding the approximate solution converging to the fixed point of the problem. We also study the solution of the nonlinear eigenvalue equation A(x, x) + B(x, x) = λx and discuss its dependency to the parameter. Our results extend and improve many known results in this field of study. We have also successfully demonstrated the application of our results to the study of nonlinear fractional differential equations with two-point boundary conditions. c 2016 All rights reserved.Keywords: Mixed monotone operator, hypo-homogeneous mixed monotone operator, existence and uniqueness, fractional differential equation.

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

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By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann-Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.

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