A nonlinear alternative of Leray–Schauder type is presented for condensing operators with closed graph. We will then use this theorem to establish new existence principles for differential and integral inclusions in Banach spaces.

In this paper we establish existence and regularity of positive solutions for a singular quasilinear elliptic system with competitive structure. The approach is based on comparison properties, a priori estimates and the Schauder’s …xed point theorem.

In this paper we use the well-known Schauder fixed point principle to obtain the existence of square-mean almost periodic solutions to some classes of nonautonomous second order stochastic differential equations on a Hilbert space.

Let X be a separable Banach space with a Schauder basis, admitting a continuous bump which depends locally on finitely many coordinates. Then X admits also a C∞-smooth bump which depends locally on finitely many coordinates.

We present an existence theorem for integral equations of UrysohnVolterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this paper using the well-known Schauder fixed point theorem we study and obtain the existence of almost periodic mild solutions to some classes of nonautonomous third-order differential equations on a separable infinite dimensional complex Hilbert space.

In this note the concept of lower and upper solutions combined with the nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first order discrete inclusions with nonlinear boundary conditions.