Uniqueness of positive radial solutions for a class of infinite semipositone 𝑝-Laplacian problems in a ball

We prove uniqueness of positive radial solutions to the p-Laplacian problem { −∆pu = λf(u) in Ω, u = 0 on ∂Ω, where ∆pu = div(|∇u|p−2∇u), p ≥ 2, Ω is the open unit ball in RN , N > 1, f : (0,∞)→ R is concave, p − sublinear at ∞ with infinite semipositone structure at 0, and λ is a large parameter. *co-authors: K. D. Chu and D. D. Hai.

[1]  R. Shivaji,et al.  Uniqueness of positive radial solutions for infinite semipositone p-Laplacian problems in exterior domains , 2019, Journal of Mathematical Analysis and Applications.

[2]  D. Hai.  On a class of singular p-Laplacian boundary value problems , 2011 .

[3]  E. N. Dancer,et al.  Uniqueness and Nonexistence of Positive Solutions to Semipositone Problems , 2006 .

[4]  P. Simon,et al.  Multiplicity for semilinear elliptic equations involving singular nonlinearity , 2006 .

[5]  R. Shivaji,et al.  Existence and uniqueness for a class of quasilinear elliptic boundary value problems , 2003 .

[6]  P. Drábek,et al.  Existence and uniqueness of positive solutions for some quasilinear elliptic problems , 2001 .

[7]  A. Castro,et al.  Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearity , 1995 .

[8]  Song-Sun Lin.  On the number of positive solutions for nonlinear elliptic equations when a parameter is large , 1991 .

[9]  E. N. Dancer.  On the Number of Positive Solutions of Weakly Non‐Linear Elliptic Equations when a Parameter is Large , 1986 .

[10]  M. Wiegner.  A uniqueness theorem for some nonlinear boundary value problems with a large parameter , 1985 .

[11]  Charles Alexander Stuart,et al.  Existence and approximation of solutions of non-linear elliptic equations , 1976 .

[12]  Charles Alexander Stuart,et al.  Existence theorems for a class of non-linear integral equations , 1974 .

[13]  W. Fulks,et al.  A singular non-linear equation , 1960 .

[14]  B. Son,et al.  A uniqueness result for a semipositone p-Laplacian problem on the exterior of a ball , 2017 .

[15]  F. J. Mancebo,et al.  Chapter 4 Singular elliptic and parabolic equations , 2006 .

[16]  Zongming Guo,et al.  Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  M. M. Coclite,et al.  On a singular nonlinear dirichlet problem , 1989 .

[18]  Jesús Ildefonso Díaz Díaz,et al.  An elliptic equation with singular nonlinearity , 1987 .

[19]  J. Díaz,et al.  Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires , 1987 .

[20]  A. Castro,et al.  Uniqueness of positive solutions for a class of elliptic boundary value problems , 1984, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[21]  Michael G. Crandall,et al.  On a dirichlet problem with a singular nonlinearity , 1977 .

[22]  Samuel Karlin,et al.  On a Theorem of P. Nowosad , 1967 .