Multiplicity of positive solutions for second-order three-point boundary value problems

2000

47 citations recorded by the source corpus.

We study the multiplicity of positive solutions for the second-order three-point boundary value problem u″+λh(t)f(u)=0, t∈(0,1), u(0)=0, αu(η)=u(1) where η: 0 < η < 1, 0 < α < 1η. The methods employed are fixed-point index theorems and Leray-Schauder degree and upper and lower solutions.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d31011e9d6e5a9abc723fcbf66813bdb73726aec

Citations in the corpus

• Solutions to Second-order Three-point Problems on Time Scales (2002, background): “This boundary value problem (1), (2) was studied by He and Ge [11] and Ma [14],[15],[16] in the case of T = R, on the unit interval; consequently these results are new for difference equations as well as for the general time scale that contains 0.”
• EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS (2003, background): “Under a variety of BCs, Lan and Webb [10] and, more recently, Ma [12] studied eigenfunctions of the special case f(t, u(t)) = g(t)h(u).”
• Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations (2009, background): “Since then a lot of attention has been paid to the study of nonlinear multi-point boundary value problems, see [12–17,19–31].”
• POSITIVE SOLUTIONS OF A THREE-POINT BOUNDARY-VALUE PROBLEM ON A TIME SCALE (2003, background): “For other references on multi-point boundary-value problems we refer the reader to the papers [16, 17, 19] and references therein.”