‎‎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, some nonexistence, existence and multiplicity of positive solutions are established for a class of singular boundary value problem. The authors also obtain the relation between the existence of the solutions and the parameter λ. The arguments are based upon the fixed point index theory and the upper and lower solutions method.

In this paper, we discuss the existence, nonexistence, and multiplicity of positive solutions for a class of singular eigenvalue problems. Some of our theorems are new, while others extend earlier results obtained by Zhang and Kong [12]. The interesting point is that the authors obtain the relation between the existence of solutions and the parameter λ. The arguments are based on the fixed poin...

Using a specially constructed cone and the fixed point index theory, this paper shows the existence of multiple positive solutions for a class of nonresonant singular boundary-value problem of second-order differential equations. The nonexistence of positive solution is also studied.

Positive solutions of systems of Hammerstein integral equations are studied by using the theory of the fixed-point index for compact maps defined on cones in Banach spaces. Criteria for the fixed-point index of the Hammerstein integral operators being 1 or 0 are given. These criteria are generalizations of previous results on a single Hammerstein integral operator. Some of criteria are new and ...

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation (|u|u) = λg(t)f(u), 0 < t < 1, where p > 1, λ > 0. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold λ < +∞, such that if 0 < λ ≤...

In this article, we study a class of boundary value problems with p-Laplacian. By using a “Green-like” functional and applying the fixed point index theory, we obtain eigenvalue criteria for the existence of positive solutions. Several explicit conditions are derived as consequences, and further results are established for the multiplicity and nonexistence of positive solutions. Extensions are ...

The second-order differential and difference boundary value problems arise in many branches of both applied and basic mathematics and have been extensively studied in the literature. We refer the reader to [1–4] for some recent results for second-order nonlinear two-point boundary value problems. The main tools used in the above works are fixed-point theorems. Avery and Peterson [1] generalize ...

In this paper, we revisit a diffusive Leslie–Gower predator–preymodel with Holling-type II functional responses and Dirichlet boundary condition. It is shown that multiple positive steady state solutions exist under certain conditions on the parameters, while for another parameter region, the positive steady state solution is unique and locally asymptotically stable. Results are proved by using...