On the solvability of a boundary value problem on the real line

Abstract

We investigate the existence of heteroclinic solutions to a class of nonlinear differential equationsgoverned by a nonlinear differential operator Φ extending the classical p-Laplacian, with right-hand side f having the critical rate of decay -1 as |t| +∞, that is f (t, ·, ·) ≈ 1 t . We prove general existence and non-existence results, as well as some simple criteria useful for right-hand side having the product structure f(t, x, x') = b(t, x)c(x, x').

Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines

“…Φ is singular. Marcelli and Papalini [20], Liu [17] and Cupini, Marcelli and Papalini [8,9] discussed the solvability of the following strongly nonlinear BVP:…”

Existence and non-existence of positive solutions of Sturm–Liouville BVPs for ODEs on whole line

“…In recent years, the existence of solutions of boundary value problems of the differential equations on whole line has been studied by many authors, see [2][3][4][5][6][7][8][9][10]17,20,22,23,27] and the references therein. In [12], Deren and Hamal investigated the existence and multiplicity of nonnegative solutions for the following integral boundary-value problem on the whole line where λ > 0 is a parameter, f, g 1 , g 2 ∈ C(IR, ×[0, ∞) × IR, [0, ∞)), q, ψ ∈ C(IR, (0, ∞)) and p ∈ C(IR, (0, ∞)) ∩ C 1 (IR).…”

Existence and non-existence of positive solutions of four-point BVPs for ODEs on whole line

“…In recent years, the existence of solutions of boundary value problems of the differential equations on whole line has been studied by many authors, see [6][7][8][9][10]12,16,[19][20][21][22][23][24] and the references therein. This paper is motivated by [15], in which the author studied, by using the Krasnoselskii's theorem in a cone, the existence of at least one or two positive solutions to the following four-point boundary value problem on finite interval ⎧ ⎨ ⎩ y (t) + a(t) f (y(t)) = 0, t ∈ (0, 1),…”