Existence Results Of Positive Solutions Research Articles

Bifurcation and positive solutions of a nonlinear fourth-order dynamic boundary value problem on time scales

This paper discusses the spectrum properties of a linear fourth-order dynamic boundary value problem on time scales and obtains the existence result of positive solutions to a nonlinear fourth-order dynamic boundary value problem. The key condition which makes nonlinear problem have at least one positive solution is related to the first eigenvalue of the associated linear problem. The proof of the main result is based upon the Krein-Rutman theorem and the global bifurcation techniques on time scales.

Existence results for fractional q-difference equations with nonlocal q-integral boundary conditions

In this paper, we discuss the existence of positive solutions for nonlocal q-integral boundary value problems of fractional q-difference equations. By applying the generalized Banach contraction principle, the monotone iterative method, and Krasnoselskii’s fixed point theorem, some existence results of positive solutions are obtained. In addition, some examples to illustrate our results are given.

Some New Existence Results of Positive Solutions to an Even-Order Boundary Value Problem on Time Scales

We consider a high-order three-point boundary value problem. Firstly, some new existence results of at least one positive solution for a noneigenvalue problem and an eigenvalue problem are established. Our approach is based on the application of three different fixed point theorems, which have extended and improved the famous Guo-Krasnosel’skii fixed point theorem at different aspects. Secondly, some examples are included to illustrate our results.

Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional <i>q</i>-Difference Equation

In this paper, we investigate the existence of positive solutions for a class of nonlinear q-fractional boundary value problem. By using some fixed point theorems on cone, some existence results of positive solutions are obtained.

Positive solutions of semi-positone nonlinear operator equations in Banach spaces with lattice structure

By using global bifurcation theories we obtain an existence result for positive solutions of some nonlinear operator equations. The main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions.

Positive solutions of m-point boundary value problems for a class of nonlinear fractional differential equations

This paper deals with the existence and multiplicity of positive solutions for a class of nonlinear fractional differential equations with m-point boundary value problems. We obtain some existence results of positive solution by using the properties of the Green’s function, u 0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator.

Positive solutions of Sturm-Liouville boundary value problems for singular nonlinear second-order impulsive integro-differential equation in Banach spaces

In this work, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for singular nonlinear second-order impulsive integro differential equation in a real Banach space. Some new existence results of positive solutions are established by applying fixed-point index theory together with comparison theorem. Some discussions and an example are given to demonstrate the applications of our main results.

Solutions of Schrödinger equations with inverse square potential and critical nonlinearity

In this paper, we are concerned with the following nonlinear Schrödinger equations with inverse square potential and critical Sobolev exponent(P)−Δu−μu|x|2+a(x)u=|u|2⁎−2u+f(x,u),u∈H1(RN), where 2⁎=2N/(N−2) is the critical Sobolev exponent, 0⩽μ<μ¯:=(N−2)24, a(x)∈C(RN). We first give a representation to the Palais–Smale sequence related to (P) and then obtain an existence result of positive solutions of (P). Our assumptions on a(x) and f(x,u) are weaker than the known cases even if μ=0.

Existence and multiplicity results to Neumann problems for elliptic equations involving the p-Laplacian

In this paper, existence results of positive solutions to a Neumann problem involving the p-Laplacian are established. Multiplicity results are also pointed out. The approach is based on variational methods.

Existence of positive solutions for a fourth order differential inclusion

We prove an existence result for positive solutions of a fourth order differential inclu- sion. The proof is accomplished through the use of Green's functions and a fixed point theorem. One of the technical assumptions is explored in detail.

Existence of Positive Solutions to Periodic Boundary Value Problems for Nonlinear Ordinary Differential Systems with Sign-changing Green Function

This paper deals with the periodic boundary value problems where is a constant and in which case the associated Greens function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping.

Existence of positive solutions to periodic boundary value problems with sign-changing Green's function

This paper deals with the periodic boundary value problems where is a constant and in which case the associated Green's function may changes sign. The existence result of positive solutions is established by using the fixed point index theory of cone mapping.

Positive solutions for multipoint boundary value problem of fractional differential equations

In this paper, we study the existence of positive solutions for a multi-point boundary value problem of nonlinear fractional differential equations. By applying a monotone iterative method, some existence results of positive solutions are obtained. In addition, an example is included to demonstrate the main result.

Neumann Boundary Value Problems with not Coercive Potential

Existence results of positive solutions for an ordinary Neumann boundary value problem are established. No asymptotic condition on the nonlinear term either at zero or at infinity is requested. The approach is based on variational methods.

Existence Results for a Nonlinear Semipositone TelegraphSystem with Repulsive Weak Singular Forces

Using the fixed point theorem of cone expansion/compression, we consider the existence results of positive solutions for a nonlinear semipositone telegraph system with repulsive weak singular forces.

Positive solutions to a two point singular boundary value problem

We employ fixed point index theory to establish existence results for positive solutions to the singular boundary value problem � −(au � ) � (t )= b(t)f(t,u(t)), t ∈ (0,1) ,

Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1), i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0&lt;α&lt;((β/2)+2π2)2,β&gt;−2π2,(α/π4)+(β/π2)+1&gt;0. The discussion is based on the fixed point index theory in cones.

Positive Solution of Singular Fractional Differential Equation in Banach Space

We investigated a singular multipoint boundary value problem for fractional differential equation in Banach space. The nonlinear term f(t, x, y) is positive and singular at x = θ and (or) y = θ. Employing regularization, sequential techniques, and diagonalization methods, we obtained some new existence results of positive solution.

Positive solutions of a nonlinear impulsive equation with periodic boundary conditions

In this paper, we investigate nonlinear second order differential equations subject to linear impulse conditions and periodic boundary conditions. Sign properties of an associated Green’s function are exploited to get existence results for positive solutions of the nonlinear boundary value problem with impulse. Upper and lower bounds for positive solutions are also given. The results obtained yield periodic positive solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.

Positive Solutions for a Class of n Th-Order m-Point Singular Boundary Value Problem

In this paper,by using Krasnosel'skill fixed point theorem,the existence result of positive solutions is established for the following nth-order m-point singular boundary value problem: where h(t) can be singular at t=0,t=1,f(t,v_0,v_1,…,v_(n-2)) may also be singular at v_i=0(i=0,1,…,n-2).