Positive solutions of singular sublinear fourth-order boundary value problems

Abstract

We give some necessary and sufficient conditions for the existence of Ca²[0,1] and C ³[0,1] positive solutions to the singular boundary value problem

where: λ∈ (0,1) is given; and p : (0,1)→ [0,∞) can be singular at both ends t = 0 and t = 1. We also give a sufficient condition for the existence of C ¹[0,1] positive solutions to the above problem. The proofs are based upon the method of lower and upper solutions for singular fourth-order boundary value problems.

Keywords:

• Singular boundary value problem
• Existence
• Schauder fixed point theorem
• Green's function
• Lower and upper solutions
• Mathematics Subject Classifications: 34B15
• 34B18

Notes

Supported by the Australian Research Council's Discovery Projects (DP0450752).

Supported by the NSFC (No.10271095), GG-110-10736-1003, NWNU-KJCXGC-212.

Supported by the NSFC (No.10271095), GG-110-10736-1003, NWNU-KJCXGC-212.

Additional information

Notes on contributors

Christopher C. Tisdell ¶

Supported by the Australian Research Council's Discovery Projects (DP0450752). Supported by the NSFC (No.10271095), GG-110-10736-1003, NWNU-KJCXGC-212.