Existence of Solutions for the Fisher-Kolmogorov Equation
Keywords:
Prime numbers, Number theory, Arithmetic functionsAbstract
In this paper we investigate the Cauchy problem for the Fisher-Kolmogorov equation for existence of global classical solutions. We give conditions under which the considered equation has at least one, at least two and at least three classical solutions. To prove our main results we propose a new approach based upon recent theoretical results.
References
[1] Agarwal RP, Meehan M, O’Regan D. Fixed Point Theory and Applications. Vol. 141. Cambridge: Cambridge University Press; 2001.
[2] Deimling K. Nonlinear Functional Analysis. Berlin, Heidelberg: Springer-Verlag; 1985.
[3] Djebali S, Mebarki K. Fixed point index for expansive perturbation of -set contraction mappings. Topol Methods Nonlinear Anal. 2019;54(2):613–40.
[4] Drábek P, Milota J. Methods in Nonlinear Analysis: Applications to Differential Equations. Basel: Birkhäuser; 2007.
[5] Georgiev S, Kheloufi A, Mebarki K. Existence of classical solutions for a class of impulsive Hamilton-Jacobi equations. Accepted in Palestine J Math.
[6] Kolmogorov AN, Petrovsky IC, Piscunov NS. Investigation of a diffusion equation connected to the growth of materials, and application to a problem in biology. Bull Univ Moscow, Ser Int Sec A. 1937;1:1–26. (In Russian)
[7] Mebarki K, Georgiev S, Djebali S, ZXennir K. Fixed Point Theorems with Applications. Boca Raton: CRC Press; 2023.
[8] Mouhous M, Georgiev S, Mebarki K. Existence of solutions for a class of first-order boundary value problems. Arch Math (Brno). 2022;58(3):141–58. doi:10.5817/AM2022-3-141
[9] Polyanin A, Manzhirov A. Handbook of Integral Equations. Boca Raton: CRC Press; 1998.
