Sign-Changing Solutions for Discrete Dirichlet Boundary Value Problem

Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems

Solutions for a nonlinear fractional boundary value problem with sign-changing Green’s function

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a...

Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity

and Applied Analysis 3 A2 there exist g x , h x , and k t 0, such that 0 ≤ f t, x ≤ k t g x h x , ∀x ∈ 0,∞ , a.e. t ∈ 0, 1 , 1.6 here g : 0,∞ → 0,∞ is continuous and nonincreasing, h : 0,∞ → 0,∞ is continuous, and h/g is nondecreasing; A3 There exist two positive constants R > r > 0 such that R > ΦR1 γ∗ ≥ r > 0, ∫1 0 k s g ( rsα−1 ) ds < ∞, R ≥ ( 1 h R g R )∫1 0 1 − s α−β−1 Γ α ( 1 − aξα−β−1 s ...

Triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities

In this paper, we study the existence of triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities. We first study the associated Green’s function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. The results of this paper are new and extent previously known results. 2000 Mathematics Subjec...

Positive solutions for discrete fractional initial value problem

‎‎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...