On the uniqueness of positive solution of an elliptic equation

This work deals with the uniqueness of positive solution for an elliptic equation whose nonlinearity satisfies a specific monotony property. In order to prove the main result, we employ a change of variable used in previous papers and the maximum principle.

[1]  J. López-Gómez,et al.  Characterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion , 2002, Advances in Differential Equations.

[2]  Haim Brezis,et al.  Sublinear elliptic equations in ℝn , 1992 .

[3]  M. Delgado,et al.  Positive solutions for the degenerate logistic indefinite superlinear problem the slow diffusion case , 2003 .

[4]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[5]  H. Amann.  On the Existence of Positive Solutions of Nonlinear Elliptic Boundary value Problems , 1971 .

[6]  T. Laetsch.  Uniqueness for sublinear boundary value problems , 1973 .

[7]  Uniqueness in a diffusion model of population biology , 1983 .

[8]  P. Hess.  On uniqueness of positive solutions of nonlinear elliptic boundary value problems , 1977 .

[9]  H. Amann.  Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces , 1976 .

[10]  Haim Brezis,et al.  Remarks on sublinear elliptic equations , 1986 .

[11]  On the structure of the positive solutions of the logistic equation with nonlinear diffusion , 2002 .

[12]  Patrizia Pucci,et al.  The strong maximum principle revisited , 2004 .

[13]  C. Bandle,et al.  The asymptotic behavior of the solutions of degenerate parabolic equations , 1987 .

[14]  Haim Brezis,et al.  Combined Effects of Concave and Convex Nonlinearities in Some Elliptic Problems , 1994 .

[15]  Morton E. Gurtin,et al.  On the diffusion of biological populations , 1977 .