Three positive solutions for a generalized Laplacian boundary value problem with a parameter

Positive solutions for nonlinear problems involving the one-dimensional ϕ-Laplacian

“…The existence of positive solutions for problems as (1.1) involving the so-called φ-Laplacian have been widely studied in the literature (see e.g. [1,2,4,5,11,14,15,16,23] and the references therein) and appear in diverse applications such as reaction-diffusion systems, nonlinear elasticity, glaciology, population biology, combustion theory, and non-Newtonian fluids, see for instance [8,10,12,17]. We mention also that these kind of problems arise naturally in the study of radial solutions for nonlinear equations in annular domains (see e.g.…”

Three positive solutions of a nonlinear Dirichlet problem with competing power nonlinearities

“…[6]). Some recent papers that study higher order multiplicity of positive solutions to nonlinear problems are [7,8,9]. In [7], a one-dimensional problem (2) with p = 2 and f λ (x, u) = λg(u) has been considered for Ω = (−1, 1).…”

“…Under some assumptions on the coefficients and the exponent γ, the existence of three positive solutions has been proved for λ belonging to an open subinterval of (0, ∞). Finally, in [9], a one-dimensional problem (2) (the authors considered a more general form of the differential operator) with f λ (x, u) = λa(x)g(u) and Ω = (0, 1) has been considered. Under various assumptions, including g(u) u p−1 in a positive neighborhood of 0, the existence of three positive solutions has been shown for λ belonging to an open subinterval of (0, ∞).…”

Multiple Positive solutions of a $(p_1,p_2)$-Laplacian system with nonlinear BCs

“…The Krasnosel'skiȋ-Guo Theorem, more in general, topological methods are a commonly used tool in the study of existence of positive solutions for the p-Laplacian equation (1.1) subject to different BCs. This is an active area of research, for example, homogeneous Dirichlet BCs have been studied in [1,5,16,25,31,37,43,47], homogeneous Robin BCs in [31,43,47], non local BCs of Dirichlet type in [3,4,6,7,9,14,24,39,41,48] and nonlocal BCs of Robin type in [14,30,32,40,42,48].…”