• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.651-675
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• 2018

We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.359-380
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• 2017

This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.187-220
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• 2016

This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.155-167
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• 2019

In this article we are concerned with some non-local problems of Kirchhoff type with Dirichlet boundary condition in Orlicz-Sobolev spaces. A result of the existence of infinitely many solutions is established using variational methods and Ricceri's critical points principle modified by Bonanno.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.255-268
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• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.1-24
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• 2008

Let $Lu=u_{tt}+u_{xxxx}$ and E be the complete normed space spanned by the eigenfunctions of L. We reveal the existence of six nontrivial solutions of a nonlinear suspension bridge equation $Lu+bu^+=1+{\epsilon}h(x,t)$ in E when the nonlinearity crosses three eigenvalues. It is shown by the critical point theory induced from the limit relative category of the torus with three holes and finite dimensional reduction method.

• East Asian mathematical journal
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• v.27 no.5
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• pp.585-595
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• 2011

In this paper, we introduce and study a new class of strongly nonlinear variational-like inequalities. Under suitable conditions, we prove the existence of solutions for the class of strongly nonlinear variational- like inequalities. By making use of the auxiliary principle technique, we suggest an iterative algorithm for the strongly nonlinear variational-like inequality and give the convergence criteria of the sequences generated by the iterative algorithm.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.443-468
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• 2008

We give a theorem of existence of six nontrivial solutions of the nonlinear Hamiltonian system $\.{z}$ = $J(H_z(t,z))$. For the proof of the theorem we use the critical point theory induced from the limit relative category of the torus with three holes and the finite dimensional reduction method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.339-342
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• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

• 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.