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 discuss the existence of solutions for a boundary value problem of second order fractional differential inclusions with four-point integral boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory. Full text

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.

The Schauder-Tychonoff theorem states that a continuous function from a compact convex subset of a locally convex topological vector space into itself must have a fixed point ([1, Chapter V, 10.5], or [2]). Using this theorem, we obtain here a stronger result, stating that a map from such a set into the surrounding vector space has a fixed point if the directions in which the points are moved s...

The original motivation for this paper is based on the natural question left open by the Gowers-Maurey solution of the unconditional basic sequence problem for Banach spaces ([12]). Recall that Gowers and Maurey have constructed a Banach space X with a Schauder basis (en)n but with no unconditional basic sequence. Thus, while every infinite dimensional Banach space contains a sequence (xn)n whi...