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Abstract
In this paper, we give existence and uniqueness results of nontrivial positive solution for the boundary value problem of the weighted and generalized Fisher's type differential equation.
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References
- R.P. Agarwal and D. O’Regan, Infinite interval problems for differential, difference and integral equations, Kluwer Academic Publisher, Dordrecht, 2001.
- O. R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Clarendon, Oxford (1975).
- O. R. Aris, Introduction to the analysis of chemical, Prentice-Hall, Englewood Cliffs, New Jersey, .1965.
- D.G. Aronson, H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial Differ. Eq. Relat. Top. 446 (1975) 5–49
- C. Bai and C. Li, Unbounded upper and lower solution method for third-order boundary value problem on the half-line, Electron. J. Differential Equations, 2009 (2009), No. 119, 1-12.
- N. Benkaci-Ali, Positive Solution for the Integral and InOnite Point Boundary Value Problem for Fractional-Order Di§erential Equation Involving a Generalized φ-Laplacian Operator, Abstract and Applied Analysis, Volume 2020, 11.
- C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
- J. Dehong, M. Feng, W. Ge; Multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity, Appl. Math. Comput. 196 (2008) 511-520.
- M. Garcia-Huidobro, R. Manasevich, F. Zanolin; Strongly nonlinear second order O.D.E.’s with rapidly growing terms, J. Math. Anal. Appl. 202 (1996), 1-26
- D. Guo, V. Lakshmikantaham; Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.
- W. Hudson and B. Zinner, Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media, Auburn university, Alabama 36849-5307 USA.
- H. Kheiri, A Mojaver and S. Shahi, Analytical solutions for the fractional Fisher’s equation, Sahand Communications in Mathematical Analysis (SCMA) Vol. 2 No. 1 (2015), 27-49.
- N.A. Kudryashov, Exact solitary waves of the Fisher equation, Phys. Lett. A 342 (1–2) (2005) 99–106.
- J. D. Murray, Mathematical biology. An introduction, Springer-Verlag, 2001, p. 556.
- Ramesh Chand Mittal and Rakesh Kumar Jain, Numerical solutions of nonlinear Fisher’s reaction–diffusion equation with modified cubic B-spline collocation method, Mathematical Sciences volume 7, Article number: 12 (2013)
- Roman Cherniha and Vasyl Dutka, Exact and numerical solutions of the generalized Fisher equation, Reports on Mathematical Physics, Volume 47, Issue 3, (2001), 393-411.
- E. Zeidler; Nonlinear Functional Analysis and its applications, Vol. I, Fixed point theorems, Springer-Verlag, New-York 1986
References
R.P. Agarwal and D. O’Regan, Infinite interval problems for differential, difference and integral equations, Kluwer Academic Publisher, Dordrecht, 2001.
O. R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Clarendon, Oxford (1975).
O. R. Aris, Introduction to the analysis of chemical, Prentice-Hall, Englewood Cliffs, New Jersey, .1965.
D.G. Aronson, H.F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial Differ. Eq. Relat. Top. 446 (1975) 5–49
C. Bai and C. Li, Unbounded upper and lower solution method for third-order boundary value problem on the half-line, Electron. J. Differential Equations, 2009 (2009), No. 119, 1-12.
N. Benkaci-Ali, Positive Solution for the Integral and InOnite Point Boundary Value Problem for Fractional-Order Di§erential Equation Involving a Generalized φ-Laplacian Operator, Abstract and Applied Analysis, Volume 2020, 11.
C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
J. Dehong, M. Feng, W. Ge; Multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity, Appl. Math. Comput. 196 (2008) 511-520.
M. Garcia-Huidobro, R. Manasevich, F. Zanolin; Strongly nonlinear second order O.D.E.’s with rapidly growing terms, J. Math. Anal. Appl. 202 (1996), 1-26
D. Guo, V. Lakshmikantaham; Nonlinear Problems in Abstract Cones, Academic Press, San Diego, 1988.
W. Hudson and B. Zinner, Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media, Auburn university, Alabama 36849-5307 USA.
H. Kheiri, A Mojaver and S. Shahi, Analytical solutions for the fractional Fisher’s equation, Sahand Communications in Mathematical Analysis (SCMA) Vol. 2 No. 1 (2015), 27-49.
N.A. Kudryashov, Exact solitary waves of the Fisher equation, Phys. Lett. A 342 (1–2) (2005) 99–106.
J. D. Murray, Mathematical biology. An introduction, Springer-Verlag, 2001, p. 556.
Ramesh Chand Mittal and Rakesh Kumar Jain, Numerical solutions of nonlinear Fisher’s reaction–diffusion equation with modified cubic B-spline collocation method, Mathematical Sciences volume 7, Article number: 12 (2013)
Roman Cherniha and Vasyl Dutka, Exact and numerical solutions of the generalized Fisher equation, Reports on Mathematical Physics, Volume 47, Issue 3, (2001), 393-411.
E. Zeidler; Nonlinear Functional Analysis and its applications, Vol. I, Fixed point theorems, Springer-Verlag, New-York 1986