International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180209Ground states solutions for modified fourth-order elliptic systems with steep well potential323334http://dx.doi.org/10.22436/jnsa.011.03.01ENLiuyang ShaoSchool of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. ChinaHaibo ChenSchool of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. ChinaIn this paper, we study the following modified quasilinear fourth-order
elliptic systems
\[
\left\{\begin{array}{lll}
&\triangle^{2}u-\triangle u+(\lambda\alpha(x)+1)u-\frac{1}{2}\triangle(u^{2})u=\frac{p}{p+q}|u|^{p-2}|v|^{q}u,~~&\mbox{in} \;~\mathbb{R}^{N}, \\
& \triangle^{2}v-\triangle v+(\lambda\beta(x)+1)v-\frac{1}{2}\triangle(v^{2})v=\frac{q}{p+q}|u|^{p}|v|^{q-2}v,~~&\mbox{in} \;~\mathbb{R}^{N},\end{array}
\right.\]
where \(\triangle^{2}=\triangle(\triangle)\) is the biharmonic operator, \(\lambda>0\), and \(2<p, 2<q,\) \(4<p+q<22^{\ast\ast}\), \(2^{\ast\ast}=\frac{2N}{N-4} \ (N\leq5)\) \((\mbox{if}~N\leq4, 2^{\ast\ast}=\infty)\) is the critical Sobolev exponent for the embedding \(W^{2,2}(\mathbb{R}^{N})\hookrightarrow L^{2^{\ast\ast}}(\mathbb{R}^{N})\). Under some appropriate assumptions on \(\alpha(x)\) and \(\beta(x)\), we obtain that the above problem has nontrivial ground state solutions via the variational methods. We also explore the phenomenon of concentration of solutions.http://isr-publications.com/jnsa/6770/download-ground-states-solutions-for-modified-fourth-order-elliptic-systems-with-steep-well-potentialInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180209Some additive mappings on Banach \({\ast}\)-algebras with derivations335341http://dx.doi.org/10.22436/jnsa.011.03.02ENJae-Hyeong BaeHumanitas College, Kyung Hee University, Yongin 17104, Republic of KoreaIck-Soon ChangDepartment of Mathematics, Chungnam National University, 99 Daehangno, Yuseong-gu, Daejeon 34134, Republic of KoreaWe take into account some additive mappings in Banach \(\ast\)-algebras with derivations.
We will first study the conditions for additive mappings with derivations on Banach \(\ast\)-algebras.
Then we prove some theorems involving linear mappings on Banach $\ast$-algebras with derivations.
So derivations on \(C^{\ast}\)-algebra are characterized. http://isr-publications.com/jnsa/6771/download-some-additive-mappings-on-banach-ast-algebras-with-derivationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180214A system of evolutionary problems driven by a system of hemivariational inequalities342357http://dx.doi.org/10.22436/jnsa.011.03.03ENLu-Chuan CengDepartment of Mathematics, Shanghai Normal University,Shanghai 200234, ChinaChing-Feng WenCenter for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80702, Taiwan; Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80702, TaiwanJen-Chih YaoCenter for General Education, China Medical University, Taichung 40402, TaiwanYonghong YaoDepartment of Mathematics, Tianjin Polytechnic University, Tianjin 300387, ChinaIn this paper, we introduce the differential system obtained by mixing a system of evolution equations and a system of hemivariational inequalities
((SEESHVI), for short). We prove
the superpositional measurability and upper semicontinuity for the solution set of a general system of hemivariational inequalities, and establish the
non-emptiness and compactness of the solution set of (SEESHVI). http://isr-publications.com/jnsa/6783/download-a-system-of-evolutionary-problems-driven-by-a-system-of-hemivariational-inequalitiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180214Weakly \(\mathbf{(s,r)}\)-contractive multi-valued operators on \(\mathbf{b}\)-metric space358367http://dx.doi.org/10.22436/jnsa.011.03.04ENLingjuan YeSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, ChinaCongcong ShenSchool of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, ChinaIn this paper we introduce the notion of weakly \((s,r)\)-contractive multi-valued operator on \(b\)-metric space and establish some fixed point theorems for this operator. In addition, an application to the differential equation is given to illustrate usability of obtained results.http://isr-publications.com/jnsa/6784/download-weakly-mathbfsr-contractive-multi-valued-operators-on-mathbfb-metric-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180214Existence of solutions for a class of second-order impulsive Hamiltonian system with indefinite linear part368374http://dx.doi.org/10.22436/jnsa.011.03.05ENQiongfen ZhangCollege of Science, Guilin University of Technology, Guilin, Guangxi 541004, P. R. ChinaWe consider a class of second-order impulsive Hamiltonian system with indefinite linear part. By using saddle point theorem in critical point theory, an existence result is obtained, which extends and improves some existing results. http://isr-publications.com/jnsa/6786/download-existence-of-solutions-for-a-class-of-second-order-impulsive-hamiltonian-system-with-indefinite-linear-partInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180214Bifurcation and periodically semicycles for fractional difference equation of fifth order375382http://dx.doi.org/10.22436/jnsa.011.03.06ENTarek F. IbrahimMathematics Department, College of Sciences and Arts for Girls in sarat Abida, King Khalid University, Saudi Arabia \(\&\) Mathematics Department, Faculty of Science, Mansoura University, Mansoura , EgyptOur paper takes into account a new bifurcation case of the cycle length and a fifth-order difference equation dynamics of
\[
y_{m+1}=\frac{y_{m} y_{m-2}^\alpha y_{m-4}^\beta+y_{m} +y_{m-2}^\alpha +y_{m-4}^\beta + \gamma }{y_{m}y_{m-2}^\alpha + y_{m-2}^\alpha y_{m-4}^\beta+y_{m} y_{m-4}^\beta+ \gamma +1} , \quad
m=0,1,2,3, \ldots,
\]
where \(\gamma \in [0, \infty )\) , \(\alpha,\beta\in \mathbb{Z^+} \), and \(y_{-4},y_{-3},y_{-1},y_{-2},y_0 \in (0, \; \infty )\) is took into consideration. The disturbance of initials lead to a distinction of cycle length principle of the non-trivial solutions of the equation. The principle of the track solutions structure for this equation is
given. The consecutive periods of negative and positive semicycles of non-trivial solutions of this equation take place periodically with only prime period fifteen and in a period with the principles represented by either \(\{3^+,1^-, 2^+, 2^-, 1^+,1^-,1^+, 4^-\}\) or \(\{3^-,1^+, 2^-, 2^+, 1^-,1^+,1^-, 4^+\}\). From this rubric we will establish that the positive fixed point has global asymptotic stability. http://isr-publications.com/jnsa/6787/download-bifurcation-and-periodically-semicycles-for-fractional-difference-equation-of-fifth-orderInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180216Some identities of degenerate Fubini polynomials arising from differential equations383393http://dx.doi.org/10.22436/jnsa.011.03.07ENSung-Soo PyoDepartment of Mathematics Education, Silla University, Busan, Republic of KoreaRecently, Kim et al. have studied degenerate Fubini polynomials
in [T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 2857--2864]. Jang and Kim presented some identities of Fubini polynomials
arising from differential equations in [G.-W. Jang, T. Kim, Adv. Studies Contem. Math.,
\({\bf 28}\) (2018), to appear]. In this paper,
we drive differential equations from the generating function of the
degenerate Fubini polynomials. In addition, we obtain some
identities from those differential equations. http://isr-publications.com/jnsa/6790/download-some-identities-of-degenerate-fubini-polynomials-arising-from-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111320180216Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems394416http://dx.doi.org/10.22436/jnsa.011.03.08ENLai-Jiu LinDepartment of Mathematics, National Changhua University of Education, Changhua, 50058, TaiwanIn this paper, we apply Theorem 3.2 of [G. M. Lee, L.-J. Lin, J. Nonlinear Convex Anal., \({\bf 18}\) (2017), 1781--1800] to study
the variational inequality over split equality fixed point problems
for three finite families of strongly quasi-nonexpansive mappings.
Then we use this result to study variational inequalities over split
equality for three various finite families of nonlinear mappings. We
give a unified method to study split equality for three various
finite families of nonlinear problems. Our results contain many
results on split equality fixed point problems and multiple sets
split feasibility problems as special cases. Our results can treat
large scale of nonlinear problems by group these problems into
finite families of nonlinear problems, then we use simultaneous
iteration to find the solutions of these problems. Our results will
give a simple and quick method to study large scale of nonlinear
problems and will have many applications to study large scale of
nonlinear problems. http://isr-publications.com/jnsa/6791/download-simultaneous-iteration-for-variational-inequalities-over-common-solutions-for-finite-families-of-nonlinear-problems