• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1817-1826
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• 2013

The existence of at least three weak solutions is established for a class of quasilinear elliptic equations involving the p(x)-biharmonic operators with Navier boundary value conditions. The technical approach is mainly based on a three critical points theorem due to Ricceri [11].

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.419-430
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• 2016

In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

• East Asian mathematical journal
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• v.39 no.1
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• pp.29-36
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• 2023

In this paper, we consider φ-Laplacian nonlocal boundary value problems with singular weight function which may not be in L¹(0, 1). The existence and nonexistence of positive solutions to the given problem for parameter λ belonging to some open intervals are shown. Our approach is based on the fixed point index theory.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.59-74
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• 2010

In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.79-95
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• 2008

The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing he Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

• East Asian mathematical journal
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• v.32 no.5
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• pp.621-633
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• 2016

We establish the existence of positive solutions to nonlocal boundary value problems with integral boundary condition and non-negative real boundary parameter by mainly using the Schauder-Fixed point theorem.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.877-882
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• 2010

In this paper, a third-order three-point boundary value problem on time scales is considered. We establish criteria for the existence of a solution and a positive solution by using the Leray-Schauder fixed point theorem. An example is also given to illustrate our results.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.25-29
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• 1996

The Debreu-Gale-Nikaido theorem [2] is a potential tool to prove the existence of a market equilibrium price. Walras' law is of a quantitative nature (i.e. it measures the value of the total excess demand), and it is interesting to note that the existence result holds true under some qualitative assumptions. In fact, the Debreu-Gale-Nikaido theorem states that the continuity of the excess demand function and Walras' law has the following implication : For some price and corresponding value of the excess demand function, it is not possible to respond with a new price system such that the value at the new price of every element in the value of the demand function associated with the old price system is strictly positive.