# Nonlinear functional analysis

@inproceedings{Browder1970NonlinearFA, title={Nonlinear functional analysis}, author={Felix Earl Browder}, year={1970} }

This manuscript provides a brief introduction to nonlinear functional analysis. We start out with calculus in Banach spaces, review differentiation and integration, derive the implicit function theorem (using the uniform contraction principle) and apply the result to prove existence and uniqueness of solutions for ordinary differential equations in Banach spaces. Next we introduce the mapping degree in both finite (Brouwer degree) and infinite dimensional (Leray-Schauder degree) Banach spaces…

## 1,325 Citations

Study on existence of solutions for some nonlinear functional-integral equations with applications

- Mathematics
- 2013

In this paper, using the technique of measure of noncompactness in Banach algebra, we prove an existence theorem for a nonlinear integral equation which contains as particular cases a lot of integral…

An Application of the Browder-Minty Theorem in a Problem of Partial Differential Equations

- Mathematics
- 2019

In this work, we will show existence of weak solution for a semilinear elliptic problem using as main tool the Browder-Minty Theorem. First, we will make a brief introduction about basic theory of…

Existence of Solutions of Boundary Value Problems for Fractional Differential Equations with p-Laplacian Operator in Banach Spaces

- Mathematics
- 2017

ABSTRACT In this paper, we consider the existence of solutions for systems of nonlinear p-Laplacian fractional differential equations whose nonlinearity contains the first-order derivative explicity…

Existence and Uniqueness of Solution for Second Order Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces

- Mathematics
- 2010

In this paper, by use of a new comparison result and monotone iterative method, the unique solution and successive approxmation of the two-point boundary value problems for nonlinear…

Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity

- MathematicsJournal of Taibah University for Science
- 2019

ABSTRACT In this paper, we will study solution existence and its stability for hybrid fractional DE with fractional integral, fractional differential derivative and Φp-operator in Caputo sense. Our…

Periodic solutions for functional differential equations with sign-changing nonlinearities

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 2010

We establish some eigenvalue criteria for the existence of non-trivial T-periodic solutions of a class of first-order functional differential equations with a nonlinearity f(x). The nonlinear term…

Solvability of Boundary Value Problems for Singular Quasi-Laplacian Differential Equations on the Whole Line

- Mathematics
- 2012

This paper is concerned with some integral type boundary value problems associated to second order singular differential equations with quasi-Laplacian on the whole line. The emphasis is put on the…

Monotone iterative technique for neutral fractional differential equation with infinite delay

- Mathematics
- 2016

In this paper, we employ the method of lower and upper solutions coupled with the monotone iterative technique to obtain existence and uniqueness of extremal mild solutions to neutral fractional…

Solvability of a recursive functional equation in the sequence Banach space

- Mathematics
- 2007

The main aim of this paper is to study the existence of solutions of the following recursive functional equation x(n) = f(n,x(n),x(n 1)) in the space l 2 , under general assumptions. The main tools…

On existence of solutions for some functional integral equations in Banach algebra by fixed point theorem

- Mathematics
- 2022

In this research, we analyze the existence of solution for some nonlinear functional integral equations using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in…

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