# On a criterion for the existence of at least four solutions of functional boundary value problems

Authors
Publication Date
Source
Czech Digital Mathematics Library
Keywords
• Keyword:Functional Boundary Conditions
• Keyword:Functional Differential Equation
• Keyword:Existence
• Keyword:Multiplicity
• Keyword:Bihari Lemma
• Keyword:Homotopy
• Keyword:Leray Schauder Degree
• Keyword:Borsuk Theorem
• Msc:47H15
• Msc:47N20
summary:A class of functional boundary conditions for the second order functional differential equation $x''(t)=(Fx)(t)$ is introduced. Here $F:C^1(J) \rightarrow L_1(J)$ is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.