Positive pseudo-symmetric solutions for a nonlocal p-Laplacian boundary value problem

Abstract

This paper is devoted to the study of the following nonlocal p -Laplacian functional differential equationsubject to multi point boundary conditions. We obtain some results on the existence of at least one (when n ∈ Z + ) or triple (when n = 0 ) pseudo-symmetric positive solutions by using fixedpoint theory in cone.

Solvability of integral boundary value problems at resonance in $R^{n}$

“…Let A = (a ij ) n×n be a square matrix of order n. α : [0, 1] → R is a bounded variation function, and 1 0 u(t) dα(t) = ( under the following assumptions: (H1) B is a diagonalization matrix, and det(I -B) = 0; (H2) 1 0 t(1t) dα(t) = 0; (H3) f : [0, 1] × R 2n → R n satisfies the Carathéodory conditions. If the condition (H 1 ) is considered, the associated linear problem -u (t) = 0, u(0) = 0, u(1) = A 1 that, when n = 1, the existence theory of integral boundary value problems for ordinary differential equations or fractional differential equations has been well studied; we refer the reader to [4,10,17,20,21,24,25,[29][30][31][32][33][34][35]37] for some recent results at non-resonance and to [2,3,16,18,22,23,27,36] for results at resonance. When n ≥ 2 and A is not a diagonal matrix, IBVP (1.1) becomes a system of ordinary differential equations with coupled boundary conditions.…”