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Cemil Tunc 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.5
In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.
Tunc, Cemil The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.5
In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.
HYBRID FIXED POINT RESULTS VIA E.A AND TANGENTIAL PROPERTIES IN METRIC SPACES
Shoaib, Muhammad,Sarwar, Muhammad,Tunc, Cemil The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.4
In this manuscript, hybrid fixed point results for four maps using (E.A) and tangential properties in the setting of metric space are studied. Application to system of functional equations is also studied.
HYBRID FIXED POINT RESULTS VIA E.A AND TANGENTIAL PROPERTIES IN METRIC SPACES
Muhammad Shoaib,Muhammad Sarwar,Cemil Tunc 호남수학회 2018 호남수학학술지 Vol.40 No.4
In this manuscript, hybrid xed point results for fourmaps using (E:A) and tangential properties in the setting of metricspace are studied. Application to system of functional equations isalso studied.
Multiplicity results of critical local equation related to the genus theory
Mohsen Alimohammady,Asieh Rezvani,Cemil Tunc 대한수학회 2023 대한수학회논문집 Vol.38 No.4
Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation \[ \begin{cases} -div [a(x, |\nabla u|) \nabla u] = \mu (b(x) |u|^{s(x) -2} - |u|^{r(x) -2})u & \text{in} ~~\Omega,\\ u=0 & \text{on}~~ \partial \Omega, \end{cases} \] where $\Omega \subseteq \mathbb{R}^N$ is a bounded domain, $\mu$ is a positive real parameter, $p$, $r$ and $s$ are continuous real functions on $\bar{\Omega}$ and $a(x, \xi)$ is of type $|\xi|^{p(x) -2}$. Next, we study boundedness and simplicity of eigenfunction for the case $a(x, |\nabla u|) \nabla u= g(x) | \nabla u|^{p(x) -2}\nabla u$, where $g\in L^{\infty}(\Omega)$ and $g(x) \geq 0$ and the case $a(x, |\nabla u|) \nabla u= (1+ \nabla u|^2)^{\frac{p(x) -2}{2}} \nabla u$ such that $p(x) \equiv p$.