Positive solutions to a class of elastic beam equations with semipositone nonlinearity

• Autorzy: Qingliu Yao
• Języki publikacji: EN

Abstrakty

EN

Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem
$u^{(4)}(t) = f(t,u(t),u'(t))$, 0 < t < 1, u(0) = u'(0) = u'(1) =u'''(1) =0,
where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the deflection of an elastic beam fixed at the left end and clamped at the right end by sliding clamps.

Kategorie tematyczne

• 34B18: Positive solutions of nonlinear boundary value problems
• 34B15: Nonlinear boundary value problems
• 34B16: Singular nonlinear boundary value problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2010
• Tom: 97
• Numer: 1
• Strony: 35-50

Daty

wydano

2010

Twórcy

autor

Qingliu Yao

• Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, P.R. China

Identyfikatory

DOI

10.4064/ap97-1-3