• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.327-334
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• 2009

By means of Riccati transformation techniques, we obtain some criteria which ensure that every solution of a nonlinear equation on time scales oscillates.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.373-378
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• 2013

In this paper, we consider two kinds of the Levenberg-Marquardt method for solve a system of nonlinear equations. We use line search on every iteration to guarantee that the Levenberg-Marquardt methods are globally convergent. Under mild conditions, we prove that while the de- scent condition can be satisfied at the iteration of the Levenberg-Marquardt method, the global convergence of the method can be established.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1453-1467
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• 2007

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1003-1013
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• 1996

The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.867-885
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• 2011

We study a class of quasilinear wave equations with strong and nonlinear viscosity. By using the perturbation method for semilinear parabolic equations, we have established the fundamental results on existence, uniqueness and continuous dependence on data of weak solutions.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.1069-1088
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• 2015

In this paper, some basic results concerning the existence, strict and nonstrict inequalities and existence of the maximal and minimal solutions are proved for a hybrid causal differential equation. Our results generalize some basic results of Leela and Laksh-mikantham [13] and Dhage and Lakshmikantham [10] respectively for the nonlinear first order classical and hybrid differential equations.

• East Asian mathematical journal
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• v.33 no.3
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• pp.323-331
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• 2017

In this paper, we consider the existence of positive solutions for eigenvalue problems of nonlinear fractional differential equations with singular weights. We give various conditions on f and apply Krasnoselskii's Cone Fixed Point Theorem. As a result, we obtain several existence and nonexistence results corresponding to ${\lambda}$ in certain intervals.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.313-328
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• 1998

In this paper we establish the equivalence between the generalized nonlinear mixed variational inequalities and the gener-alized resolvent equations. This equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized vari-ational inequalities. We also discuss the convergence analysis of the propose algorithms. As special cases we obtain various known re-sults from our results.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.447-454
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• 2014

Two necessary and sufficient conditions for the oscillation of the bounded solutions of the second-order nonlinear delay differential equation $$(a(t)x^{\prime}(t))^{\prime}+q(t)f(x[{\tau}(t)])=0$$ are obtained by constructing the sequence of functions and using inequality technique.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.741-748
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• 2012

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.