In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

In this paper, we study the existence of positive solutions for nonlinear four-point singular boundary-value problems for higher-order equation with the p-Laplacian operator. Using the fixed-point index theory, we find conditions for the existence of one solution, and of multiple solutions.

In this paper some existence and nonexistence results for positive solutions are obtained for second-order boundary value problem −u + Mu = f(t, u), t ∈ (0, 1) with Neumann boundary conditions u(0) = u(1) = 0, where M > 0, f ∈ C([0, 1] × R, R). By making use of fixed point index theory in cones, some new results are obtained. Full text

We present an alternative approach to the vector version of Krasnosel’skiĭ compression–expansion fixed point theorem due Precup, which is based on index. It allows us obtain new general versions this and also multiplicity results. emphasize that all them are coexistence theorems for operator systems, means every component points obtained non-trivial. Finally, these applied results concerning ex...

Let U be an open subset of a locally compact metric ANR X and let f : U → X be a continuous map. In this paper we study the fixed point index of the map that f induces in the n-symmetric product of X, Fn(X). This index can detect the existence of periodic orbits of period ≤ n of f , and it can be used to obtain the Euler characteristic of the n-symmetric product of a manifold X, χ(Fn(X)). We co...

Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions. Retractos, ı́ndice de punto fijo y ecuaciones d...

In this paper we analyze a nonlocal reaction-diffusion model which arises from the modeling of competition of phytoplankton species with incomplete mixing in a water column. The nonlocal nonlinearity in the model describes the light limitation for the growth of the phytoplankton species. We first consider the single-species case and obtain a complete description of the longtime dynamical behavi...

Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy p...

The existence of fixed point in orthogonal metric spaces has been initiated by Eshaghi and et. al [7]. In this paper, we prove existence and uniqueness theorem of fixed point for mappings on $varepsilon$-connected orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point for analytic function of one complex variable. The paper concludes with some i...

By means of calculation of the fixed point index in cone we consider the existence of one or two positive solutions for the fourth-order boundary value problem with variable parameters { u(t) + B(t)u′′(t)−A(t)u(t) = f(t, u(t), u′′(t)), 0 < t < 1, u(0) = u(1) = u′′(0) = u′′(1) = 0, where A(t), B(t) ∈ C[0, 1] and f(t, u, v) : [0, 1]× [0,∞)×R → [0,∞) is continuous.