• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.147-160
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• 2012

In this paper, we establish some sufficient conditions for the existence of positive solutions for a class of multi-point boundary value problem for fractional functional differential equations involving the Caputo fractional derivative. Our results are based on two fixed point theorems. Two examples are also provided to illustrate our main results.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.333-341
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• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.733-745
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• 2013

In this paper, we first propose a new technique of the functional iterative methods VIM (Variational iteration method) and NHPM (New homotopy perturbation method) for solving two-point boundary value problems, and then we compare their numerical results with those of the finite difference method (FDM).

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.29-40
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• 2009

Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.637-650
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• 2008

New sufficient conditions for the existence of at least one solution of Neumann type boundary value problems for second order nonlinear differential equations $$\array{\{{p(t)\phi(x'(t)))'=f(t,x(t),\;x(\tau_1(t)),\;{\cdots},\;x(\tau_m(t))),\;t\in[0,T],\\x'(0)=0,\;x'(T)=0,}\,}$$, are established.

• 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.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.527-541
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• 2006

In this paper, an existence theorem for a nonlinear two point boundary value problem of second order differential equations in Banach algebras is proved using a nonlinear alternative based on Leray-Schauder alternative.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.323-334
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• 2010

We give a theorem for the existence of at least three solutions for the fourth order elliptic boundary value problem with the square growth variable coefficient nonlinear term. We use the variational reduction method and the critical point theory for the associated functional on the finite dimensional subspace to prove our main result. We investigate the shape of the graph of the associated functional on the finite dimensional subspace, (P.S.) condition and the behavior of the associated functional in the neighborhood of the origin on the finite dimensional reduction subspace.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.9-21
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• 2018

We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.