• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.83-98
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• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• 대한수학회보
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• 제48권5호
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• pp.1047-1061
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• 2011

In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.

• 대한수학회보
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• 제55권6호
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• pp.1639-1657
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• 2018

In this paper, we initiate the study of boundary value problems involving Hilfer fractional derivatives. Several new existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating our results are also presented.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.205-230
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• 2015

A class of periodic type boundary value problems of coupled impulsive fractional differential equations are proposed. Sufficient conditions are given for the existence of solutions of these problems. We allow the nonlinearities p(t)f(t, x, y) and q(t)g(t, x, y) in fractional differential equations to be singular at t = 0, 1 and be involved a sup-multiplicative-like function. So both f and g may be super-linear and sub-linear. The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the theorems.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.711-721
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• 2010

Values of the parameter $\lambda$ are determined for which there exist positive solutions of the system of boundary value problems, $u^{(n)}+{\lambda}p(t)f(\upsilon)=0$, $\upsilon^{(n)}+{\lambda}q(t)g(u)=0$, for $t\;{\in}\;[a,b]$, and satisfying, $u^{(i)}(a)=0$, $u^{(\alpha)}(b)=0$, $\upsilon^{(i)}(a)=0$, $\upsilon^{(\alpha)}(b)=0$, for $0\;{\leq}\;i\;{\leq}\;n-2$ and $1\;{\leq}\;\alpha\;\leq\;n-1$ (but fixed). A well-known Guo-Krasnosel'skii fixed point theorem is applied.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.65-71
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• 2019

This paper is concerned with the existence of positive solutions of the nonlinear Neumann boundary value problems $$\{u^{{\prime}{\prime}}+a(t)u={\lambda}b(t)f(u),\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$, where $a,b{\in}C[0,1]$ with $a(t)>0,\;b(t){\geq}0$ and the Green's function of the linear problem $$\{u^{{\prime}{\prime}}+a(t)u=0,\;t{\in}(0,1),\\u^{\prime}(0)=u^{\prime}(1)=0$$ may change its sign on $[0,1]{\times}[0,1]$. Our analysis relies on the Leray-Schauder fixed point theorem.

• Kyungpook Mathematical Journal
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• 제47권4호
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• pp.569-578
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• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.621-633
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• 2014

In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

• Korean Journal of Mathematics
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• 제17권4호
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• 대한수학회보
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• 제47권2호
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• pp.411-422
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• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.