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Equations with discontinuous nonlinear semimonotone operators

Nguyen Buong (1999)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type x + K F ( x ) = 0 with the discontinuous semimonotone operator F . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in L p ( Ω ) are given for illustration.

Evolution in a changing environment: existence of solutions

P. Rybka, Q. Tang, D. Waxman (2003)

Colloquium Mathematicae

We establish the existence of solutions of an intrinsically nonlinear differential-integral equation that arises from the mathematical modelling of the evolution of an asexual population in a changing environment. The main objective is to pave the way for a rigorous analysis of the linear stability of travelling wave solutions of the corresponding problem.

Existence and Asymptotic Stability of Solutions of a Perturbed Quadratic Fractional Integral Equation

Darwish, Mohamed, Henderson, Johnny (2009)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 45G10, 45M99, 47H09We study the solvability of a perturbed quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions which are defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. Finally, we give an example to illustrate our abstract results.

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

Annales Polonici Mathematici

Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation ϕ ( x ) = λ [ x , x + ω ] Ω K ( x , y ) h ( y ) f ( y , ϕ ( y - τ ( y ) ) ) d y , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

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