International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Some common fixed point theorems in dislocated metric spaces8692http://dx.doi.org/10.22436/jnsa.008.02.01ENSamiaBennaniDepartment of Mathematics and Informatics, Faculty of Sciences Ben M'sik, BP. 7955, Sidi Othmane, University Hassan II-Mohammédia, Casablanca, Morocco.HichamBourijalDepartment of Mathematics and Informatics, Faculty of Sciences Ben M'sik, BP. 7955, Sidi Othmane, University Hassan II-Mohammédia, Casablanca, Morocco.SoufianeMhannaDepartment of Mathematics and Informatics, Faculty of Sciences Ben M'sik, BP. 7955, Sidi Othmane, University Hassan II-Mohammédia, Casablanca, Morocco.Driss ElMoutawakilLaboratory of Applied Mathematics and Technology of Information and Communication, Faculty Polydisciplinary of Khouribga, BP. 145, University Hassan I - Settat, Khouribga, Morocco.Our purpose in this paper is to establish some new common fixed point theorems for four self-mappings of
a dislocated metric space.
http://isr-publications.com/jnsa/1903/download-some-common-fixed-point-theorems-in-dislocated-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328New results of positive solutions for second-order nonlinear three-point integral boundary value problems9398http://dx.doi.org/10.22436/jnsa.008.02.02ENZhijianYaoDepartment of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China.In this paper, we investigate the existence of positive solutions for second-order nonlinear three-point integral
boundary value problems. By using the Leray-Schauder fixed point theorem, some sufficient conditions
for the existence of positive solutions are obtained, which improve the results of literature Tariboon and
Sitthiwirattham [J. Tariboon, T. Sitthiwirattham, Boundary Value Problems, 2010 (2010), 1-11].
http://isr-publications.com/jnsa/1750/download-new-results-of-positive-solutions-for-second-order-nonlinear-three-point-integral-boundary-value-problemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Positive solutions for Caputo fractional differential equations involving integral boundary conditions99109http://dx.doi.org/10.22436/jnsa.008.02.03ENYongWangSchool of Science, Jiangnan University, Wuxi 214122, China.YangYangSchool of Science, Jiangnan University, Wuxi 214122, China.In this work we study integral boundary value problem involving Caputo differentiation
\[
\begin{cases}
^c D^q_t u(t)= f(t,u(t)),\,\, 0<t<1,\\
\alpha u(0)-\beta u(1)=\int^1_0 h(t)u(t)dt, \gamma u'(0)-\delta u'(1)\int^1_0 g(t)u(t)dt,
\end{cases}
\]
where \(\alpha,\beta,\gamma,\delta\)
are constants with \(\alpha>\beta>0,\gamma>\delta>0, f\in C([0,1]\times \mathbb{R}^+,\mathbb{R}), g,h\in C([0,1],\mathbb{R}^+)\) and \( ^c D^q_t\)
is the standard Caputo fractional derivative of fractional order \(q(1 < q < 2)\). By using some fixed point
theorems we prove the existence of positive solutions.
http://isr-publications.com/jnsa/1751/download-positive-solutions-for-caputo-fractional-differential-equations-involving-integral-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations110129http://dx.doi.org/10.22436/jnsa.008.02.04ENWenguiYangMinistry of Public Education, Sanmenxia Polytechnic, Sanmenxia, Henan 472000, China.In this paper, we study the existence of positive solutions for a class of coupled integral boundary value
problems of nonlinear semipositone Hadamard fractional differential equations
\[D^\alpha u(t) + \lambda f(t, u(t), v(t)) = 0,\quad D^\alpha v(t) + \lambda g(t, u(t), v(t)) = 0,\quad t \in (1, e),\quad \lambda > 0\]
\[u^{(j)}(1) = v^{(j)}(1) = 0, 0 \leq j \leq n - 2; u(e) = \mu\int^e_1 v(s) \frac{ds}{ s} , v(e) = \nu\int^e_1 u(s) \frac{ds}{ s},\]
where \(\lambda,\mu,\nu\) are three parameters with \(0<\mu<\beta\) and \(0<\nu<\alpha,\quad \alpha,\beta\in (n - 1; n]\) are two real numbers
and \(n\geq 3, D^\alpha, D^\beta\) are the Hadamard fractional derivative of fractional order, and \(f; g\) are sign-changing
continuous functions and may be singular at \(t = 1\) or/and \(t = e\). First of all, we obtain the corresponding
Green's function for the boundary value problem and some of its properties. Furthermore, by means of the
nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorems, we derive an interval
of \(\lambda\) such that the semipositone boundary value problem has one or multiple positive solutions for any \(\lambda\)
lying in this interval. At last, several illustrative examples were given to illustrate the main results.
http://isr-publications.com/jnsa/1752/download-positive-solutions-for-singular-coupled-integral-boundary-value-problems-of-nonlinear-hadamard-fractional-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Coupled fixed point theorems for compatible mappings in partially ordered \(G\)-metric spaces130141http://dx.doi.org/10.22436/jnsa.008.02.05ENJianhuaChenDepartment of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.XianjiuHuangDepartment of Mathematics, Nanchang University, Nanchang, 330031, P. R. China.In this paper, we prove coupled coincidence and coupled common fixed point theorems for compatible
mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of
some existing results. We also give an example to support our results.
http://isr-publications.com/jnsa/1814/download-coupled-fixed-point-theorems-for-compatible-mappings-in-partially-ordered-g-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Uniqueness and global exponential stability of almost periodic solution for Hematopoiesis model on time scales142152http://dx.doi.org/10.22436/jnsa.008.02.06ENZhijianYaoDepartment of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601,China.This paper deals with almost periodic Hematopoiesis dynamic equation on time scales. By applying a
novel method based on the fixed point theorem of decreasing operator, we establish sufficient conditions
for the existence of unique almost periodic positive solution. Particularly, we give iterative sequence which
converges to the almost periodic positive solution. Moreover, we investigate global exponential stability of
the almost periodic positive solution by means of Gronwall inequality.
http://isr-publications.com/jnsa/1815/download-uniqueness-and-global-exponential-stability-of-almost-periodic-solution-for-hematopoiesis-model-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328Coupled fixed point theorems with respect to binary relations in metric spaces153162http://dx.doi.org/10.22436/jnsa.008.02.07ENMohammad SadeghAsgariDepartment of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran.BaharakMousaviDepartment of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran.In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with
a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in
this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed
to hold on elements that are comparable in the binary relation. Next on the basis of the coupled fixed
point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix
equation.
http://isr-publications.com/jnsa/1816/download-coupled-fixed-point-theorems-with-respect-to-binary-relations-in-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-19018220150328The elliptic sinh-Gordon equation in the half plane163173http://dx.doi.org/10.22436/jnsa.008.02.08ENGuenboHwangDepartment of Mathematics, Daegu University, Gyeongsan Gyeongbuk 712-714, KoreaBoundary value problems for the elliptic sinh-Gordon equation formulated in the half plane are studied
by applying the so-called Fokas method. The method is a significant extension of the inverse scattering
transform, based on the analysis of the Lax pair formulation and the global relation that involves all known
and unknown boundary values. In this paper, we derive the formal representation of the solution in terms
of the solution of the matrix Riemann-Hilbert problem uniquely defined by the spectral functions. We also
present the global relation associated with the elliptic sinh-Gordon equation in the half plane. We in turn
show that given appropriate initial and boundary conditions, the unique solution exists provided that the
boundary values satisfy the global relation. Furthermore, we verify that the linear limit of the solution
coincides with that of the linearized equation known as the modified Helmhotz equation.http://isr-publications.com/jnsa/1817/download-the-elliptic-sinh-gordon-equation-in-the-half-plane