References
- Bandle C, Punzo F, Tesei A. Existence and nonexistence of patterns on Riemannian manifolds. J Math Anal Appl. 2012;387:33–47.
- Farina A, Sire Y, Valdinoci E. Stable solutions of elliptic equations on Riemannian manifolds. J Geometric Anal. 2013;23:1158–1172.
- Jimbo S. On a semilinear diffusion equation on a Riemannian manifold and its stable equilibrium solutions. Proc Japan Acad Ser A. 1984;60:349–352.
- Nascimento AS, Gonçalves AC. Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature. Electron J Differ Equ. 2010;67:1–18.
- Punzo F. The existence of patterns on surfaces of revolution without boundary. Nonlinear Anal. 2013;77:94–102.
- Rubinstein J, Wolansky G. Instability results for reaction diffusion equations over surfaces of revolutions. J Math Anal Appl. 1994;187:485–489.
- Sonego M. Stability result of a reaction-diffusion problem with mixed boundary conditions and applications to some symmetric cases. J Math Anal Appl. 2018;466:1190–1210.
- Matano H. Asymptotic behavior and stability of solutions of semilinear diffusion equations. Publ RIMS Kyoto Univ. 1979;15:401–454.
- Yanagida E. Stability of stationary distributions in a space-dependent population growth process. J Math Biol. 1982;15:37–50.
- Kamalia PZ, Sakaguchi S. A construction of patterns with many critical points on topological tori. Nonlinear Differ Equ Appl. 2020;27:39.
- Henry D. Geometric theory of semilinear parabolic equations. Berlin: Springer: 1981; (Springer Lecture Notes in Mathematics, Vol. 840).
- Deimling K. Nonlinear functional analysis. New York: Dover Publications; 2010.
- Nirenberg L.. Topics in nonlinear functional analysis, Revised reprint of the 1974 original, Courant Lecture Notes in Mathematics, 6, American Mathematical Society, Providence (RI), 2001.
- Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. 2nd ed., New York: Springer; 1983.