• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.355-367
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• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.261-280
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• 2005

We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.61-70
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• 2001

Certain elliptic interacting system involving symbiotic is considered. The sufficient conditions for the existence of positive solutions of system is provided for four different types of interaction among three species by using the method of decomposing operator.

• East Asian mathematical journal
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• v.30 no.3
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• pp.335-353
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• 2014

We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.815-827
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• 2012

The existence of $n$ positive solutions is established for second order multi-point boundary value problem at resonance where $n$ is an arbitrary natural number. The proof is based on a theory of fixed point index for A-proper semilinear operators defined on cones due to Cremins.

• 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.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.551-563
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• 2017

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $$u^{{\Delta}{\nabla}}(t)+a(t)f(t,u(t))=0,\;t{\in}(0,T),\;{\beta}u(0)-{\gamma}u^{\Delta}(0)=0,\;u(T)={\sum_{i=1}^{m-2}}\;a_iu({\xi}_i),\;m{\geq}3$$, where $a(t){\in}C_{ld}((0,T),\;[0,+{\infty}))$, $f{\in}C([0,T]{\times}[0,+{\infty}),\;(-{\infty},+{\infty}))$, the nonlinear term f is allowed to change sign. We obtain several existence theorems of positive solutions for the above boundary value problems. In particular, our criteria generalize and improve some known results [15] and the obtained conditions are different from related literature [14]. As an application, an example to demonstrate our results is given.