Multiple positive solutions for a class of nonlinear boundary value problems

Pairs of positive solutions for nonlinear elliptic equations with the p-Laplacian and a nonsmooth potential

“…In this section we produce a second positive solution for problem (2). To do this we need to strengthen a little the hypotheses and also generalize a recent interesting result about local minimizers of smooth functionals of Brezis-Nirenberg [1] to the present nonsmooth and nonlinear setting.…”

“…2 hold and x 0 ∈ W 1, p 0 (Z ) is a local C 1 0 (Z)-minimizer of ψ, i.e., there exists r > 0 such that ψ(x 0 ) ≤ ψ(x 0 + y) for all y ∈ C 1 0 (Z) with y C 1 0 (Z) ≤ r, then x 0 is also a local minimizer of ψ in W 1, p…”

“…We refer to the works of Brown-Budin [2], Correa [7], Dancer [8], De Figueiredo [10], De FigueiredoLions [11], Hirano [20], Lions [30], and the references therein. The study of the corresponding problem for nonlinear equations driven by the p-Laplacian differential operator lags behind.…”

Positive solutions of sub-superlinear Sturm–Liouville problems

“…Motivated by some ideas in [2][3][4]6,10,14], in Section 2 we introduce the notion of a strict lower/upper solution and establish a result of Leray-Schauder degree on the ordered intervals induced by the pairs of strict lower and upper solutions. Applying the result and the fixed point index theory in cones, in Section 3 we obtain the global existence results of positive solutions for problem (1.1) with the sub-superlinear terms.…”

Positive solutions of superlinear boundary value problems

“…Problem (1.1) with / independent of u was studied in [2,3,5,6,8,11]. For general / and boundary conditions of the second or third kind ((3, 5^ 0) existence results were established in [8,11].…”