• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.845-860
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• 2010

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.1-12
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• 2015

This paper is concerned with boundary value problems for systems of n-th order dynamic equations on time scales. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.305-320
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• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.249-281
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• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.875-883
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• 2009

At least two positive solutions of a first-order periodic boundary value problem with impulse are obtained by establishing a new cone and the theorem of fixed point index. And at the end of this paper we give an example to illustrate the application of our main results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1445-1460
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• 2010

In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.249-260
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• 2007

By variational methods, we prove the existence of positive solutions of a class of indefinite weight semilinear elliptic boundary value problems on critical Sobolev exponent.

• 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 the Korean Mathematical Society
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• v.61 no.3
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• pp.445-459
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• 2024

In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.