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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2010 | 97 | 1 | 35-50

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

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.

35-50

wydano
2010

### Twórcy

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