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Positive solutions of nonlinear elliptic singular boundary value problems in a ball
Lokenath Debnath,Xingye Xu 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
This paper deals with existence of positive solutions of non-linear elliptic singular boundary value problems in a ball. It is shown thatresults of Grandall et al. [1] and [2] follow as special cases of our resultsproved in this article.
Yan Sun,Jizhou Zhang,Lokenath Debnath 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.1
In this paper, we consider the existence of multiple positive solutions for the second order nonlinear boundary value problem on the half-line [수식] where [수식] is continuous. Some weaker conditions are imposed on g yields the existence of at least three symmetric positive solutions.
Luo, Jiaowan,Debnath, Lokenath 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1
Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7]are generalized and improved.
OSCILLATIONS OF SOLUTIONS OF SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATIONS WITH IMPULSES
Jin, Chuhua,Debnath, Lokenath 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.24 No.1
Some Kamenev-type oscillation criteria are obtained for a second order quasilinear damped differential equation with impulses. These criteria generalize and improve some well-known results for second order differential equations with land without impulses. In addition, new oscillation criteria are also obtained to generalize and improve known results. Two examples of applications are given to illustrate the theory.
SMALL AMPLITUDE WAVE IN SHALLOW WATER OVER LINEAR AND QUADRATIC SLOPING BEDS
Bhatta, Dambaru D.,Debnath, Lokenath 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.
OSCILATION OF SECOND ORDER QUASILINEAR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES
Luo, Weidong,Luo, Jiaowan,Debnath, Lokenath 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.13 No.1
Sufficient conditions for oscillation of all solutions of a class of second-order quasilinear delay differential equations with fixed moments of impulse effect are found.