• Nonlinear Functional Analysis and Applications
• /
• v.28 no.3
• /
• pp.601-612
• /
• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Communications of the Korean Mathematical Society
• /
• v.13 no.1
• /
• pp.37-59
• /
• 1998

We prove that solutions $u^\epsilon$ for the mixed hyperbolic-elliptic system of conservation laws with the viscosity term are total variation bounded uniformly in $\epsilon$ and that the solution $u^\epsilon$ converges to the solution for the mixed hyperbolic-elliptic Riemann problem as $\epsilon \to 0$.

• Communications of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.207-214
• /
• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• Journal of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.85-114
• /
• 1998

We prove the existence of solutions of the Reimann problem for a system of conservation laws of mixed type using the method of vanishing viscosity term.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.365-375
• /
• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.411-422
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.4
• /
• pp.561-569
• /
• 2002

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation of Sobolev type with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.111-123
• /
• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.261-269
• /
• 2009

We adopt the idea of $C\check{a}dariu$ and Radu to prove the stability of Jordan triple linear derivations and we take account of the Jacobson radical range problem for linear derivations.

• Kyungpook Mathematical Journal
• /
• v.53 no.2
• /
• pp.257-271
• /
• 2013

In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.