Nontrivial solutions of m-point boundary value problems for singular second-order differential equations with a sign-changing nonlinear term
- Liu, Lishan
- Liu, Bingmei
- Wu, Yonghong
DOIAbstract
AbstractThis paper concerns the existence of nontrivial solutions for the following singular m-point boundary value problem with a sign-changing nonlinear term {(Lu)(t)+h(t)f(t,u)=0,0<t<1,u(0)=0,u(1)=∑i=1m−2aiu(ξi), where (Lu)(t)=(p̃(t)u′(t))′+q(t)u(t),0<ξ1<ξ2<⋯<ξm−2<1, ai∈[0,+∞), h(t) is allowed to be singular at t=0,1, and f:[0,1]×(−∞,+∞)→(−∞,+∞) is a sign-changing continuous function and may be unbounded from below. By applying the topological degree of a completely continuous field and the first eigenvalue and its corresponding eigenfunction of a special linear operator, some new results on the existence of nontrivial solutions for the above singular m-point boundary value problem are obtained. An example is then given to demonstrate th...
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