Multiple symmetric positive solutions for a second order boundary value problem

Abstract

Abstract. For the second order boundary value problem, y + f (y) = 0, 0 ≤ t ≤ 1, y(0) = 0 = y(1), where f : R → [0, ∞), growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions.

On Solutions of the Matrix Equation A ∘ l X = B with respect to Jin1 2021Journal of Mathematics2000View full textAdd to dashboardCite

“…For example, there have been a lot of researches about equations on economic theory [2], automation and information sciences [3][4][5], system and control theory [6][7][8], physics [9,10], and computing sciences [11,12]. For these fields, the numerical approximation solutions [13], least squares solutions [14], symmetric positive [15], and definite solutions [16] under various conditions can be obtained by direct or iterative methods. Furthermore, matrix equations are the basis of numerical calculation and are very good at dealing with arrays that are smaller than three dimensions.…”

Existence of Positive Solutions to Singular φ-Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function

“…Consequently, the nonlinearity h(t) f (t, u) in the Equation (1) may not satisfy the L 1 -Carathéodory condition. When ϕ(s) = s and q ≡ h ≡ 1, Henderson and Thompson [38] proved the existence of at least three symmetric positive solutions to problem (1) subject to Dirichlet boundary conditions u(0) = u(1) = 0 (i.e.,α 1 =α 2 = 0) under the assumptions on the nonlinear term…”

On the symmetric positive solutions of nonlinear fourth order ordinary differential equations with four-point boundary value conditions: a fixed point theory approach

“…Li and Zhang [13], and Henderson and Thompson [12] studied the multiple symmetric positive solutions of second order system of ordinary differential equations. Feng et al [8] studied the existence of multiple symmetric positive solutions to the system of four-point boundary-value problems with onedimensional P-Laplacian.…”