Abstract
In this paper we study the structure of all solutions to the boundary value problem, which is the open problem D of Ambrosetti, Brezis and Cerami [1] $$ -u'' = \lambda |u|^{q-1}u+|u|^{p-1}u, \quad t\in [a, b], \ \ u(a)=u(b)=0, $$ where $0 <q <1 <p,$ $ \lambda >0 .$ We obtain a complete characterization of its solutions and the bifurcation graph. By perturbation, we show also instablity of the structure of the solutions for the above problem (see Figure 3).
Citation
Yuanji Cheng. "On an open problem of Ambrosetti, Brezis and Cerami." Differential Integral Equations 15 (9) 1025 - 1044, 2002. https://doi.org/10.57262/die/1356060761
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