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

Qingliu Yao. "Positive solutions to a class of elastic beam equations with semipositone nonlinearity." Annales Polonici Mathematici 97.1 (2010): 35-50. <http://eudml.org/doc/280455>.

@article{QingliuYao2010,
abstract = {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 $u^\{(4)\}(t) = f(t,u(t),u^\{\prime \}(t))$, 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.},
author = {Qingliu Yao},
journal = {Annales Polonici Mathematici},
language = {eng},
number = {1},
pages = {35-50},
title = {Positive solutions to a class of elastic beam equations with semipositone nonlinearity},
url = {http://eudml.org/doc/280455},
volume = {97},
year = {2010},
}

TY - JOUR
AU - Qingliu Yao
TI - Positive solutions to a class of elastic beam equations with semipositone nonlinearity
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 1
SP - 35
EP - 50
AB - 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 $u^{(4)}(t) = f(t,u(t),u^{\prime }(t))$, 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.
LA - eng
UR - http://eudml.org/doc/280455
ER -