(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study the positive solutions of the semilinear elliptic equation cases Lu+g(x,u)u=0 &in& Ω, Bu=0 &on& ∂Ω, caseswhere Ω ⊂R^N is a bounded smooth domain, L is an elliptic operator, B is a general boundary operator and g(·, ·) is a continuous function. This is a general problem proposed by Amann [Arch. Rational Mech. Anal. 44 (1972)], Cac [J. London Math. Soc. 25 (1982)] and Hess [Math. Z. 154 (1977)]. We obtain various uniqueness results when the nonlinearity function g satisfies some additional conditions.