Existence and uniqueness theorems for some fourth order fully quasilinear boundary value problems

Abstract

Let be a function satisfying Caratheodary's conditions and . This paper is concerned with the problem of existence and uniqueness of solutions for the fully quasilinear boundary value problems

,with either . The conditions on the nonlinearity are related to the linear eigenvalue problems , with either .

Keywords:

• Fully quasilinear
• fourth order boundary value problem
• linear eigenvalue problem
• elastic beam
• simply-supported ends
• end clamped by sliding clamps

^†The Work was supported the part by the Applied mathematics Benefitics Subprogram of the Energy research, U.S. Department of energy, UNder Contract W 31-109 Eng 38 Under the Faculty Re Leave Program

^†Permanent address: Department of Mathematical Sciences, Northern Illinois University, Dekall, II. 60115.

^†The Work was supported the part by the Applied mathematics Benefitics Subprogram of the Energy research, U.S. Department of energy, UNder Contract W 31-109 Eng 38 Under the Faculty Re Leave Program

^†Permanent address: Department of Mathematical Sciences, Northern Illinois University, Dekall, II. 60115.

Notes

^†The Work was supported the part by the Applied mathematics Benefitics Subprogram of the Energy research, U.S. Department of energy, UNder Contract W 31-109 Eng 38 Under the Faculty Re Leave Program

^†Permanent address: Department of Mathematical Sciences, Northern Illinois University, Dekall, II. 60115.