In “zero-parameter” or classical Nielsen fixed point theory one studies Fix(f) := {x ∈ X | f(x) = x} where f : X → X is a map. In case X is an oriented compact manifold and f is transverse to the identity map, idX , Fix(f) is a finite set each of whose elements carries a natural sign, ±1, the index of that fixed point. The set Fix(f) is partitioned into Nielsen classes. Adding the indices withi...

in which the second derivative may occur nonlinearly. Positive solutions for the case f (t,u,u′,u′′) = g(t)h(u) have been studied by Ma [15] and Webb [20, 21], when f (t,u,u′,u′′) = h(t,u) by He and Ge [5] and also by Lan [11]. The case f (t,u,u′,u′′) = g(t)h(u,u′) has been studied by Feng [4]. The results in [4, 15] are obtained by means of Krasnosel’skiı̆’s theorem [8], the ones in [5] use Leg...

In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of posit...

where τ, σ , and c are constants in R with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T(> 0)-periodic function in t > 0, and for an arbitrary bounded domain E ⊂ R, g(t,x) is a Lipschitz function in [0,T] × E, p ∈ C(R,R), p(t +T) = p(t), and ∫ T 0 p(t)dt = 0. They obtained some sufficient conditions to guarantee the existence, at least a T-periodic solution, for this system. But, for the existence of pe...

In this paper, the existence of fuzzy solutions for first and second order nonlocal impulsive neutral functional differential equations are studied using Banach fixed point theorem. We used the techniques of fuzzy set theory, functional analysis, and Hausdorff metric. Example is provide to illustrate the theory.

Existence of nontrivial nonnegative equilibrium solutions for age structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive...

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

In this paper, we study existence of mild solutions for a second order impulsive neutral functional differential equations with state-dependent delay. By using a fixed point theorem for condensing maps combined with theories of a strongly continuous cosine family of bounded linear operators, we prove the main existence theorems. As applications of these obtained results, some practical conseque...

This paper investigates the existence of at least two positive solutions for the following high-order fractional semipositone boundary value problem (SBVP, for short) with coupled integral boundary value conditions:  D0+u(t) + λf(t,u(t), v(t)) = 0, t ∈ (0, 1), D0+v(t) + λg(t,u(t), v(t)) = 0, t ∈ (0, 1), u(j)(0) = v(j)(0) = 0, j = 0, 1, 2, · · · ,n− 2, Dα−1 0+ u(1) = λ1 ∫η1 0 v(t)...

A fixed point theorem for condensing maps due to Martelli combined with theories of a strongly continuous cosine family of bounded linear operators is used to investigate the existence of solutions to second order impulsive neutral functional integrodifferential inclusions with infinite delay in Banach spaces.