The Stability Results for a Singular System of Generalized p-Fisher-Kolmogoroff Steady State Type
Stability Results for a Singular System
DOI:
https://doi.org/10.31258/jomso.v2i1.26Keywords:
Stability, Fisher-Kolmogoroff steady state type, singular p-LaplacianAbstract
In the present paper, we are interested in the study of the stability results of nontrivial positive weak solutions for the generalized p-Fisher-Kolmogoroff nonlinear steady state problem involving the singular p-Laplacian operator. We provide a simple proof to establish that every positive solution is stable (unstable) under some certain conditions.
References
Murray, J., 1989., Mathematical Biology, I. An Introduction, Third Edition, Springer, New York.
Khafagy, S., Serag, H., 2022, Stability of positive weak solution for generalized weighted p-Fisher-Kolmogoroff nonlinear stationary-state problem. European Journal of Mathematical Analysis, Volume 2 :88.
Lan, K., 2017, Population models with quasi-yield harvest rates, Mathematical Biosciences and Engineering, Volume 14, pp. 467-490.
Khafagy, S., Sadeghi, Z., 2024, Existence of positive weak solution for a weighted system of autocatalytic reaction steady state type, Eur. J. Math. Appl., Volume 4 (11), pp. 1-7.
Flores, I., 2004, A resonance phenomenon for ground states of an elliptic equation of Emden-Fowler type, Jour. Diff. Eqn., Volume 198, pp. 1-15.
Khafagy, S., Rasouli, S., Serag, H., 2023, Existence results for fractional Fisher-Kolmogoroff steady state problem, Eur. J. Math. Appl., Volume 3, pp. 1-7.
Shi, J., Zhitao, Z, 2005, Lectures on solution set of semilinear elliptic equations (in Tokyo Metropolitan University).
Goddard II, J., Shivaji, R., 2014, Diffusive logistic equation with constant yield harvesting and negative density dependent emigration on the boundary, J. Math. Anal. Appl., Volume 414 (2), pp. 561-573.
Lan, K. Q., Wu, J. H., 2003, Travelling wavefronts of scalar reaction–diffusion equations with and without delays, Nonlinear Analysis: Real World Applications, Volume 4, pp.173–188.
Afrouzi, G. Sadeeghi, Z., 2008, Stability results for a class of elliptic problems, International Journal of Nonlinear Science, Volume 6 (2), pp. 114-117.
Khafagy, S., Ezzat, A., 2024, Existence and stability of positive weak solutions for a class of chemically reacting systems. Eur. J. Math. Appl., Volume 4 (2), pp. 1-12.
Afonso, D.G., Iacopetti, A., Pacella, F., 2024, Energy Stability for a Class of Semilinear Elliptic Problems, J. Geom. Anal., Volume 34 (75), pp. 1-43.
Karatson, I., Simon, P., 2001, On the stability properties of nonnegative solutions of semilinear problems with convex or concave nonlinearity, Journal of Computational and Applied Mathematics, Volume 131, pp. 497-501.
Maya, C. Shivaji, R., 1998, Instability of nonnegative solutions for a class of semilinear elliptic boundary value problems, J. Comput. Appl. Math., Volume 88, pp. 125-128.
Tertikas, A., 1992, Stability and instability of positive solutions of semilinear problems, Proc. Amer. Math. Soc., Volume 114, pp. 1035-1040.
Voros, I. 2004, Stability properties of nonnegative solutions of semilinear symmetric cooperative systems, Electronic Jour. Diff. Eqns., Volume 2004 (105), pp. 1-6.
Ali, I., Castro, A., Shivaji, R., 1993, Uniqueness and stability of nonnegative solutions for semipositone problems in a ball, Proc. Amer. Math. Soc., Volume 117, pp. 775-782.
Brown, K., Shivaji, R., 1991, Instability of nonnegative solutions for a class of semipositone problems, Proc. Amer. Math. Soc., Volume 112, pp. 121-124.
Afrouzi, G., Rasouli, S., 2006, Stability properties of non-negative solutions to a non-autonomous p-Laplacian equation, Chaos, Solitons and fractals, Volume 29, pp. 1095-1099.
Khafagy, S., 2015, On the stability of positive weak solution for weighted p-Laplacian nonlinear system, New Zealand Journal of Mathematics, Volume 45, pp. 39-43.
Khafagy, S., Serag, H., 2020, On the stability of positive weak solution for (p,q)-Laplacian nonlinear system, Applied Mathematics E-Notes, Volume 20, pp. 108-114.
Khafagy, S., Serag, H., 2018, Stability results of positive weak solution for singular p-Laplacian nonlinear system, J. Appl. Math. & Informatics, Volume 36, pp. 173-179.
Atkinson, C, Ali., K., 1992, Some boundary value problems for the Bingham model, J. Non-Newton. Fluid Mech., Volume 41, pp. 339-363.
Khafagy, S., 2016, Maximum Principle and Existence of Weak Solutions for Nonlinear System Involving Singular p-Laplacian Operators, J. Part. Diff. Eq., Volume 29, pp. 89-101.
Xuan, B., 2003, Existence results for a superlinear singular equation of Caffarelli-Kohn-Nirenberg type, Bolet´ın de Matem´aticas, Volume X, pp. 47-58.
Khafagy, S., Serag, H., 2020, On the existence of positive weak solution for nonlinear system with singular weights, Journal of Contemporary Math-ematical Analysis (Armenian Academy of Sciences), Volume 55 (4), pp. 259-267.
Farkas, G. Simon, P., 2001, Stability properties of positive solutions to partial differential equations with delay, Electron. J. Diff. Eqn., Volume 2001 (64), pp. 1-8.
Khafagy, S., El-Zahrani, E., Serag, H., 2020, Existence and uniqueness of weak solution for nonlinear weighted (p, q)-Laplacian system with application on an optimal control problem, Jordan Journal of Mathematics and Statistics (JJMS), Volume 15 (4A), pp. 983-998.
