Semi-stable and extremal solutions of reaction equations involving the $p$-Laplacian

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A Multiplicity Result for the p-Laplacian Involving a Parameter (2008, background): “There are some recent papers that deal with the compactness of the branches of solutions of similar equations which are also relevant in the context of this paper: Cabré and Sanchon [5] considered nonnegative solutions of −Δpu = f(x, u).”
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 (2008, background): “0,λb). The ﬁrst important question is to know if λb = λ∗.One of the main results of this article is the extension of the well-known result of [15] relative to the case p= 2,improving also a result of [19] for p>1. Theorem 1.3 Assume that gsatisﬁes (1.2) and gis convex near Λ, and f ∈ Lr (Ω),r>”