Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type

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Positive solutions of nonlocal boundary value problems involving integral conditions (2008, methodology): “The results of [21] apply to S and give the above statements with S in place of T , we then apply Theorem 2.”
A third order boundary value problem subject to nonlinear boundary conditions (2010, methodology): “4), Graef and Webb make use of a careful analysis of the Green function kλ combined with an earlier theory developed by Webb and co-authors [29], [30].”
Spectral properties and nodal solutions for second-order, m-point, boundary value problems (2007, methodology): “Finally, we use the global bifurcation theorem to obtain nodal solutions (that is, sign-changing solutions with a specified number of zeros) of the above problem, under various conditions on the asymptotic behaviour of f .”
Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions (2010, unknown): “1) if u ∈ Cn−2[0, 1] ∩ Cn(0, 1), u(n−1)(0+) and u(n−1)(1−) exist, and u satisfies the BVP (1.”
Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach (2006, methodology): “It is often possible to verify (UPE) when g ≡ 1 directly from the differential equation, see [28, 30].”
Solutions of nonlinear equations in cones and positive linear operators (2010, methodology): “which played a useful role in [22], and we now show that the conditions (C1)–(C3) imply that L̃ is u0-positive relative to (K0, P ).”