Double positive solutions of a three-point boundary value problem for the one-dimensional p-Laplacian

Abstract We study the existence of positive solutions for the equation (φp(u′))′ + e(t) ƒ (u) = 0 , where, φp(υ) ≔ |υ| p−2 υ, p > 1 , subject to nonlinear three-point boundary conditions. We show the existence of at least two positive solutions by using a three-functionals fixed-point theorem in a cone.

[1]  J.‐Y. Wang,et al.  On the Existence of Positive Solutions to a Three‐Point Boundary Value Problem for the One‐Dimensional p‐Laplacian , 1997 .

[2]  Abdou Kouider Ben-Naoum,et al.  On the existence and multiplicity of positive solutions of the $p$-Laplacian separated boundary value problem , 1997, Differential and Integral Equations.

[3]  Junyu Wang.  The existence of positive solutions for the one-dimensional $p$-Laplacian , 1997 .

[4]  A Remark on Some Three‐Point Boundary Value Problems for the One‐Dimensional p‐Laplacian , 2002 .

[5]  Manuel del Pino,et al.  A homotopic deformation along p of a Leray-Schauder degree result and existence for (¦u′¦p − 2u′)′ + ƒ(t, u) = 0, u(0) = u(T) = 0, p > 1 , 1989 .

[6]  D. Jiang,et al.  A Unified Approach to Some Two-Point, Three-Point, and Four-Point Boundary Value Problems with Carathéodory Functions , 1997 .

[7]  Chuanzhi Bai,et al.  Existence of multiple positive solutions for nonlinear m-point boundary-value problems , 2003, Appl. Math. Comput..

[8]  C. Coster.  Pairs of positive solutions for the one-dimensional p -Laplacian , 1994 .

[9]  Junyu Wang,et al.  Multiple positive solutions for the one-dimensional p -Laplacian , 2000 .

[10]  Johnny Henderson,et al.  Twin solutions of boundary value problems for ordinary differential equations and finite difference equations , 2001 .

[11]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[12]  Allan Peterson,et al.  Three positive fixed points of nonlinear operators on ordered banach spaces , 2001 .