Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities

Abstract

i 1 α i < 1, and f ∈ C 1 R\{0}, R ∩ C R, R satisfies f s s > 0 for s / 0, and f 0 ∞, where f 0 lim |s| → 0 f s /s. We investigate the global structure of nodal solutions by using the Rabinowitz's global bifurcation theorem.

Linear Sturm–Liouville problems with general homogeneous linear multi‐point boundary conditions

“…Then in addition to the conclusion in Part (a), SLP (1.1), (3.1) also has a positive eigenvalue λ p (c) which satisfies that λ p (c) < μ [1] p (c). Moreover, the eigenfunction y p (c) associated with λ p (c) belongs to…”

“…(1.1) and the Dirichlet BC y(a) = y(b) = 0. We also let μ [1] n ∞ n=0 and μ [2] n ∞ n=0 be the n-th eigenvalues of the SLPs consisting of Eq. (1.1) and the two-point BCs…”

Global Structure of Positive Solutions for Some Second-Order Multipoint Boundary Value Problems

“…The existence and multiplicity of nontrivial solutions for multipoint boundary value problems have been extensively considered (including positive solutions, negative solutions, or sign-changing solutions) by using the fixed point theorem with lattice, fixed point index theory, coincidence degree theory, Leray-Schauder continuation theorems, upper and lower solution method, and so on (see and references therein). On the other hand, some scholars have studied the global structure of nontrivial solutions for second-order multipoint boundary value problems (see [26][27][28][29][30][31][32] and references therein).…”

“…Motivated by [1,[26][27][28][29][30][31][32], we shall investigate the global structure of positive solutions of the boundary value problem (1). In [1], the authors only have studied the existence of positive solutions, but in this paper, we prove that the set of nontrivial positive solutions of the boundary value problem (1) possesses an unbounded connected component.…”

Reactivity of Oxygen Radical Anions Bound to Scandia Nanoparticles in the Gas Phase: CH Bond Activation

“…The existence of nodal solutions of BVPs with nonlocal BCs has also received a lot of attention in research. We refer the reader to 1, 3, 6, 7, 11–13, 16–18 for some recent work on this topic. In particular, many researchers have been working on the existence of nodal solutions of the BVP consisting of the equation and the multi‐point BC where \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$a,b\in {\mathbb {R}}$\end{document} with a < b .…”