Existence Of Triple Positive Solutions Research Articles

Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable

In this article, based on further investigation of the properties of the Green function, together with a fixed point theorem due to Avery-Peterson, height functions on special bounded sets are constructed to obtain the existence of triple positive solutions for higher-order fractional integral boundary value problems. The nonlinearity permits singularities both on the time and the space variables.

Existence of Triple Positive Solutions to a Four-Point Boundary Value Problem of a Fractional Differential Equations

In this paper, the existence result of at least triple positive solutions to a boundary value problem of a fractional differential equations is achieved by means of the Avery-Peterson fixed point theorem and the careful analysis of the associate Green's function in which the derivative of unknown function is involved in the nonlinear term explicitly. An example illustrating our main result is given. Our results complement the previous work in the area of the positive solutions of fractional differential equations.

Triple positive solutions for fractional differential equation boundary value problems at resonance

By using the theory of fixed point index, the existence of triple positive solutions to a class of resonant fractional differential equation boundary value problems is deduced. Some new height functions and the spectral theory are also used for seeking the positive solutions. The nonlinearity involves an arbitrary fractional derivative and permits singularity.

Triple positive solutions for nonlocal fractional differential equations with singularities both on time and space variables

In this paper, different height functions of the nonlinear term on special bounded sets together with Leggett–Williams and Krasnosel’skii fixed point theorems are employed to establish the existence of triple positive solutions for a class of higher-order fractional differential equations with integral conditions. The singularities are with respect not only to the time but also to the space variables.

Existence of Three Positive Solutions of Semipositone Boundary Value Problems on Time Scales

In this paper, we consider the existence of triple positive solutions for the second order semipositone m-point boundary value problem on time scales. We emphasize that the nonlinear term f may take a negative value.

Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations withp-Laplacian

We establish the existence of triple positive solutions of anm-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with ap-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend and improve the known results.

Triple positive solutions for a class of third-order p-Laplacian singular boundary value problems

In this work, we study the existence of triple positive solutions for one-dimensional p-Laplacian singular boundary value problems $$\begin{array}{l}(\phi_p(y''(t)))'+f(t)g(t,\,y(t),\,y'(t),\,y''(t))=0,\quad 0<t<1,\\[3pt]ay(0)-by'(0)=0,\qquad cy(1)+dy'(1)=0,\qquad y''(0)=0,\end{array}$$ where φp(s)=|s|p−2s, p>1, g:[0, 1]×[0, +∞)×R2⟶[0, +∞) and f:(0, 1)⟶[0, +∞) are continuous. The nonlinear term f may be singular at t=0 and/or t=1. Firstly, Green’s function for the associated linear boundary value problem is constructed. Then, by making use of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the above boundary value problem. The interesting point is that the nonlinear term g involved with the first-order and second-order derivatives explicitly.

Triple Positive Solutions for a Type of Second-Order Singular Boundary Problems

This paper deals with the existence of triple positive solutions for a type of second-order singular boundary problems with general differential operators. By using the Leggett-Williams fixed point theorem, we establish an existence criterion for at least three positive solutions with suitable growth conditions imposed on the nonlinear term.

Triple positive solutions of a boundary value problem for nonlinear singular second-order differential equations of mixed type withp-Laplacian

In this paper, we establish the existence of triple positive solutions of a two-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator. We also demonstrate that the results obtained can be applied to study certain higher order mixed boundary value problems. Finally, an example is given to demonstrate the use of the main results of this paper.

Triple positive solutions to third order three-point BVP with increasing homeomorphism and positive homomorphism

In this paper, we investigate the existence of triple positive solutions for nonlinear differential equations boundary value problems with increasing homeomorphism and positive homomorphism operator. By using fixed point theorems in cones, we establish results on the existence of three positive solutions with suitable growth conditions imposed on the nonlinear term. As applications, two examples are given to demonstrate our result. The conclusions in this paper essentially extend and improve the known results.

The existence of three positive solutions of [formula omitted]-point boundary value problems for some dynamic equations on time scales

In this paper, we define a new operator which improves and generalizes a p -Laplacian operator for some p > 1 . By using this operator, we consider the existence of triple positive solutions of m -point boundary value problems for some dynamic equations on time scales [ φ ( p ( t ) u Δ ( t ) ) ] ∇ + a ( t ) f ( u ( t ) ) = 0 , t ∈ [ 0 , T ] T κ ∩ T k , u ( 0 ) − B 0 ( ∑ i = 1 m − 2 α i u Δ ( ξ i ) ) = 0 , u Δ ( T ) = 0 , where φ : R → R is an increasing homeomorphism and positive homomorphism and φ ( 0 ) = 0 . We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term by using a new fixed-point theorem.

Three positive solutions to initial-boundary value problems of nonlinear delay differential equations

In this paper, we consider the existence of triple positive solutions to the boundary value problem of nonlinear delay differential equation (�(x 0 (t))) 0 +a(t)f(t,x(t),x 0 (t),xt) = 0, 0 < t < 1, x0 = 0, x(1) = 0, where � : R ! R is an increasing homeomorphism and positive homomorphism with �(0) = 0, and xt is a function in C(( �,0),R) defined by xt(�) = x(t + �) for � � � � 0. By using a fixed-point theorem in a cone introduced by Avery and Peterson, we provide sufficient conditions for the existence of triple positive solutions to the above boundary value problem. An example is also presented to demonstrate our result. The conclusions in this paper essentially extend and improve the known results.

The Existence of Triple Positive Solutions of Nonlinear Four-point Boundary Value Problem with p-Laplacian

This paper deals with a class of singular p-Laplacian equation (φ_p(u′(t)))′+a(t)f(t,u(t),u′(t)) = 0,0t1 subject to the following nonlinear boundary conditionsαφ_p(u′(0)) -βφ_p(u′(e)) = 0,γφ_p(u(1)) +δφ_p(u′(η)) = 0, whereφ_P(x) = |x|~(p-2)x,p1.By using the Avery-Peterson fixed point theorem,sufficient conditions for the existence of at least three positive solutions to the boundary value problem mentioned above are established.The recent results are generalized and improved.

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.

Existence of triple positive solutions for a third-order three-point boundary value problem

In this paper we investigate the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem u ‴ ( t ) = a ( t ) f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) ) , 0 < t < 1 , u ( 0 ) = δ u ( η ) , u ′ ( η ) = 0 , u ″ ( 1 ) = 0 , where δ ∈ ( 0 , 1 ) , η ∈ [ 1 / 2 , 1 ) are constants. f : [ 0 , 1 ] × [ 0 , ∞ ) × R 2 → [ 0 , ∞ ) , q : ( 0 , 1 ) → [ 0 , ∞ ) are continuous. First, Green’s function for the associated linear boundary value problem is constructed, and then, by using a fixed-point theorem due to Avery and Peterson, we establish results on the existence of triple positive solutions to the boundary value problem.

Some new results on the existence of positive solutions for the one-dimensional [formula omitted]-Laplacian boundary value problems on time scales

This paper is devoted to using the Leggett–Williams fixed point theorem to derive some sufficient conditions for the existence of triple positive solutions to a type of p -Laplacian boundary value problems on time scales. The interesting point is that the nonlinear term f depends on the first-order delta derivative explicitly.

Existence of triple positive solutions for multi-point boundary value problems with a one dimensional p-Laplacian

In this paper, we consider the existence of multiple positive solutions for multi-point boundary value problems with a one dimensional p -Laplacian { ( ϕ p ( u ′ ( t ) ) ) ′ + q ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , 0 < t < 1 u ( 0 ) = ∑ i = 1 m − 2 α i u ( ξ i ) , u ( 1 ) = ∑ i = 1 m − 2 β i u ( ξ i ) , where ϕ p ( s ) = | s | p − 2 s , p > 1 , α i ≤ β i ( 1 ≤ i ≤ m − 2 ) ∈ [ 0 , ∞ ) , ∑ i = 1 m − 2 α i , ∑ i = 1 m − 2 β i ∈ ( 0 , 1 ) , 0 < ξ 1 < ξ 2 < ⋯ < ξ m − 2 < 1 . By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.

Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equationΔ2x(k−1)+q(k)f(k,x(k),Δx(k))=0, fork∈{1,2,…,n−1}, subject to the following two boundary conditions:x(0)=x(n)=0orx(0)=Δx(n−1)=0, wheren≥3.

Triple positive solutions for boundary value problems on infinite intervals

This paper deals with the existence of triple positive solutions for Sturm–Liouville boundary value problems of second-order nonlinear differential equation on a half line. By using a fixed point theorem in a cone due to Avery–Peterson, we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term.

Existence of triple positive solutions to a class of p-Laplacian boundary value problems

By using Leggett–Williams' fixed-point theorem, a class of p-Laplacian boundary value problem is studied. Sufficient conditions for the existence of triple positive solutions are established.