We consider the existence of bound states for the coupled elliptic system ∆u1 − λ1u1 + μ1u 3 1 + βu 2 2u1 = 0 in R n , ∆u2 − λ2u2 + μ2u 3 2 + βu 2 1u2 = 0 in R n , u1 > 0, u2 > 0, u1, u2 ∈ H (R). where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum C ⊂ R5+ × H (R) × H(R) of solutions (λ1, λ2, μ1, μ2, β, u1, u2) bifurcating from the set of semi...

In the paper we construct a topological fixed-point theory for a class of set-valued maps which appears in natural way in boundary value problems for differential inclusions. Our construction is based upon the notion of (U, V )-approximation in the sense of Ben-El-Mechaiekh and Deguire. As applications we consider initial-value problems for nonlinear evolution inclusions of the type x′(t) ∈ −A(...

This paper investigates the existence of positive solutions for a sixth-order m-point boundary value problem with three variable parameters. Many problems in the theory of elastic stability can be handled by the method of multi-point problems. By using the fixed point theorem and operator spectral theorem, we give a new existence result.

*Correspondence: [email protected] 1School of Mathematics and Physics, Changzhou University, Changzhou, 213164, China 2College of Science, Hohai University, Nanjing, 210098, China Full list of author information is available at the end of the article Abstract In this paper we compute the fixed point index for A-proper semilinear operators under certain boundary conditions. The proof is based ...

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using  the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...

in this paper, we prove some coupled coincidence point theorems for mappings with the mixedmonotone property and obtain the uniqueness of this coincidence point. then we providing useful examples in nash equilibrium.

Many situations can be modeled as solutions of systems of simultaneous equations. If the functions of these equations monotonically increase in all bound variables, then the existence of extremal fixed point solutions for the equations is guaranteed. Among all solutions, these fixed points uniformly take least or greatest values for all bound variables. Hence, we call them homogeneous fixed poi...

Some results on the existence of solution for certain fuzzy equations are revised and extended. In this paper, we establish the existence of a solution for the fuzzy equation Ex2 +Fx+G= x, where E, F, G, and x are positive fuzzy numbers satisfying certain conditions. To this purpose, we use fixed point theory, applying results such as the wellknown fixed point theorem of Tarski, presenting some...