112 research outputs found
Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations
This paper studies the boundary value problems for the fourth-order nonlinear singular difference equations Ī4u(iā2)=Ī»Ī±(i)f(i,u(i)), iā[2,T+2], u(0)=u(1)=0, u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone
Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions
In this paper, we consider a four-point coupled boundary value problem for systems of the nonlinear semipositone fractional differential equation
\begin{gather*}\left\{ \begin{array}{ll}
\mathbf{D}_{0+}^\alpha u+\lambda f(t,u,v)=0,\quad 0<t<1, \lambda >0,\\
\mathbf{D}_{0+}^\alpha v+\lambda g(t,u,v)=0,\\
u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\
u(1)=av(\xi), v(1)=bu(\eta), \xi,\eta\in(0,1)
\end{array}\right.\end{gather*}
where is a parameter, satisfy , , is a real number and , and is the Riemann-Liouville's fractional derivative, and are continuous and semipositone. We derive an interval on such that for any lying in this interval, the semipositone boundary value problem has multiple positive solutions
Multiple Positive Solutions of a Second Order Nonlinear Semipositone m
In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uĪā(t)+a(t)uĪ(t)+b(t)u(t)+Ī»q(t)f(t,u(t))=0, tā(0,1)𝕋, u(Ļ(0))=0, u(Ļ(1))=āi=1m-2Ī±iu(Ī·i). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone
Singular positone and semipositone boundary value problems of nonlinear fractional differential equations
We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problem where Ī¼ > 0, a, and f are continuous, Ī± ā 3, 4 is a real number, and D Ī± 0 is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results
Applications of Schauderās Fixed Point Theorem to Semipositone Singular Differential Equations
We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauderās fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007)
. In some suitable weak singularities, the existence of periodic solutions may help
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