Electronic Journal of Differential Equations
Permanent URI for this collectionhttps://hdl.handle.net/10877/86
The Electronic Journal of Differential Equations is hosted by the Department of Mathematics at Texas State University. Since its foundation in 1993, this e-journal has been dedicated to the rapid dissemination of high quality research in mathematics.
Journal Website: http://ejde.math.txstate.edu/
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Browsing Electronic Journal of Differential Equations by Author "Addou, Idris"
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Item Boundary-value Problems for the One-dimensional p-Laplacian with Even Superlinearity(Southwest Texas State University, Department of Mathematics, 1999-03-08) Addou, Idris; Benmezai, AbdelhamidThis paper is concerned with a study of the quasilinear problem −(|u'|p−2u')' = |u|p − λ, in (0, 1), u(0) = u(1) = 0, where p >1 and λ ∈ ℝ are parameters. For λ > 0, we determine a lower bound for the number of solutions and establish their nodal properties. For λ ≤ 0, we determine the exact number of solutions. In both cases we use a quadrature method.Item Exact Multiplicity Results for Quasilinear Boundary-value Problems with Cubic-like Nonlinearities(Southwest Texas State University, Department of Mathematics, 2000-01-01) Addou, IdrisWe consider the boundary-value problem -(φp(u'))' = λf(u) in (0,1) u(0) = u(1) = 0, where p > 1, λ > 0 and φp(x) = |x|p-2x. The nonlinearity ƒ is cubic-like with three distinct roots 0 = α < b < c. By means of a quadrature method, we provide the exact number of solutions for all λ > 0. This way we extend a recent result, for p = 2, by Korman et al. [17] to the general case p > 1. We shall prove that when 1 < p ≤ 2 the structure of the solution set is exactly the same as that studied in the case p = 2 by Korman et al. [17], and strictly different in the case p > 2.Item Exactness Results for Generalized Ambrosetti-Brezis-Cerami Problem and Related One-dimensional Elliptic Equations(Southwest Texas State University, Department of Mathematics, 2000-11-02) Addou, Idris; Benmezai, Abdelhamid; Bouguima, Sidi Mohammed; Mohammed, DerhabWe consider the boundary problem -(φp(u'))' = φα(u) + λφβ(u) in (0, 1) u(0) = u(1) = 0 where φp(x) = |x|p-2 x, p, α, β > 1 and λ ∈ ℝ*. We give the exact number of solutions for all λ and most values of α, β, p > 1. In the particular case where 1 < β < p = 2 < α, we resolve completely a problem suggested by A. Ambrosetti, H. Brezis and G. Cerami and which was partially solved by S. Villegas.Item Multiplicity of Solutions for Quasilinear Elliptic Boundary-value Problems(Southwest Texas State University, Department of Mathematics, 1999-06-16) Addou, IdrisThis paper is concerned with the existence of multiple solutions to the boundary-value problem -(φp(u'))' = λφq(u) + ƒ(u) in (0, 1) , u(0) = u(1) = 0, where p, q > 1, φx(y) = |y|x−2y, λ is a real parameter, and ƒ is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.Item Multiplicity Results for Classes of One-dimensional p-Laplacian Boundary-value Problems with Cubic-like Nonlinearities(Southwest Texas State University, Department of Mathematics, 2000-07-03) Addou, IdrisWe study boundary-value problems of the type -(φp(u'))' = λƒ(u), in (0, 1) u(0) = u(1) = 0, where p > 1, φp(x) = |x|p-2 x, and λ > 0. We provide multiplicity results when ƒ behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter q > 1. We shall show hos changes in the position of q with respect to p lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that ƒ is half-odd; a condition generalizing the usual oddness. We use a quadrature method.