In this paper, we establish the existence of a solution for a coupled system of threepoint fractional order boundary value problems by applying the Schauder fixed point theorem in a Banach space under suitable conditions. Mathematics subject classification (2010): 34A34, 34B15.

We study the existence of positive solutions of the nonlinear fourth order problem u(x) = λa(x)f(u(x)), u(0) = u′(0) = u′′(1) = u′′′(1) = 0, where a : [0, 1] → R may change sign, f(0) > 0, and λ > 0 is sufficiently small. Our approach is based on the Leray–Schauder fixed point theorem.

In this paper we prove the existence of weak periodic solutions for a nonlinear parabolic equations with the Robin periodic boundary condition. The aim will be achieved by reformulating the problem in abstract form and applying some results of the maximal monotone mapping theory joint with the Schauder fixed point theorem.

Using the Schauder fixed point theorem, we prove an existence of positive solutions for the fractional differential problem in the half line R+ = (0,∞): Du = f(x, u), lim x→0+ u(x) = 0, where α ∈ (1, 2] and f is a Borel measurable function in R+ × R+ satisfying some appropriate conditions.

In this study, conditions for the existence of at least one solution to a nonlinear first-order nonlocal initial value problem on time scales are discussed. The results extend previous work in the continuous case to the discrete, quantum, and general time scales setting, and are based on the Leray-Schauder fixed point theorem.

In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.

In this paper we investigate the existence of mild solutions defined on a semiinfinite interval for initial value problems for a differential equation with a nonlocal condition. The results is based on the Schauder-Tychonoff fixed point theorem and rely on a priori bounds on solutions.

In this paper, we study the existence and nonexistence of positive solutions a system Riemann–Liouville fractional differential equations with ϱ-Laplacian operators, supplemented coupled nonlocal boundary conditions containing Riemann–Stieltjes integrals, derivatives various orders, parameters. We apply Schauder fixed point theorem in proof result.

An optimal control problem for a semilinear parabolic partial differential equation with memory is considered. The well-posedness as well the first and second order differentiability of state established by means Schauder fixed point theorem implicity function theorem. For corresponding quadratic cost functional, existence proved. necessary conditions are presented, including investigation adjo...

In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which undelayed part admits an operator. We discuss problems by utilizing theory operators, Schauder fixed point theorem Banach theorem. Some new results on considered equation are obtained infinite internal [0,+?). end, applied to a cla...