Applications of Schauder’s Fixed Point Theorem to Singular Differential Equations
نویسندگان
چکیده
In this paper, we study the existence of positive periodic solutions to second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results show that in some situations weak singularities can help create periodic solutions, as pointed out by Torres [J. Differential Equations 232 (2007) 277–284].
منابع مشابه
Singular Cauchy Initial Value Problem for Certain Classes of Integro-Differential Equations
The singular Cauchy problem for first-order differential and integro-differential equations resolved or unresolved with respect to the derivatives of unknowns is fairly well studied see, e.g., 1–16 , but the asymptotic properties of the solutions of such equations are only partially understood. Although the singular Cauchy problems were widely considered by using various methods see, e.g., 1–13...
متن کامل$L^p$-existence of mild solutions of fractional differential equations in Banach space
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
متن کاملSolvability of boundary value problems for fractional order elastic beam equations
*Correspondence: [email protected] Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou, 510320, P.R. China Abstract In this article, the existence results for solutions of a boundary value problem for nonlinear singular fractional order elastic beam equations are established. The analysis relies on the well-known Schauder’s fixed point theorem. MSC: 92D25; 34A37;...
متن کاملAnalytic Solutions for Iterative Functional Differential Equations
Because of its technical difficulties the existence of analytic solutions to the iterative differential equation x′(z) = x(az + bx(z) + cx′(z)) is a source of open problems. In this article we obtain analytic solutions, using Schauder’s fixed point theorem. Also we present a unique solution which is a nonconstant polynomial in the complex field.
متن کاملAn existence result for n^{th}-order nonlinear fractional differential equations
In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.
متن کامل