Instability of nonnegative solutions for a class of semipositone problems

Authors:
K. J. Brown and R. Shivaji

Journal:
Proc. Amer. Math. Soc. **112** (1991), 121-124

MSC:
Primary 35B35; Secondary 35B05, 35J65, 35P30

MathSciNet review:
1043405

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the boundary value problem

**unstable**.

**[1]**K. J. Brown and P. Hess,*Stability and uniqueness of positive solutions for a semi-linear elliptic boundary value problem*, Differential Integral Equations**3**(1990), no. 2, 201–207. MR**1025173****[2]**Alfonso Castro and R. Shivaji,*Nonnegative solutions for a class of nonpositone problems*, Proc. Roy. Soc. Edinburgh Sect. A**108**(1988), no. 3-4, 291–302. MR**943804**, 10.1017/S0308210500014670**[3]**Alfonso Castro and R. Shivaji,*Nonnegative solutions for a class of radially symmetric nonpositone problems*, Proc. Amer. Math. Soc.**106**(1989), no. 3, 735–740. MR**949875**, 10.1090/S0002-9939-1989-0949875-3**[4]**K. J. Brown, Alfonso Castro, and R. Shivaji,*Nonexistence of radially symmetric nonnegative solutions for a class of semi-positone problems*, Differential Integral Equations**2**(1989), no. 4, 541–545. MR**996760****[5]**Alfonso Castro and R. Shivaji,*Nonnegative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric*, Comm. Partial Differential Equations**14**(1989), no. 8-9, 1091–1100. MR**1017065**, 10.1080/03605308908820645**[6]**D. H. Sattinger,*Monotone methods in nonlinear elliptic and parabolic boundary value problems*, Indiana Univ. Math. J.**21**(1971/72), 979–1000. MR**0299921**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1991-1043405-5

Article copyright:
© Copyright 1991
American Mathematical Society