Nonlinear Boundary Value Problems for Second Order Differential Inclusions

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

“…for Φ-Laplacian operators, and recently also the study of singular or non-surjective differential operators has become object of an increasing interest (see, i.e., [1][2][3][4][5][6][7][8][9][10]). …”

“…As it easy to check, the best function K C satisfying condition (8) in [11] is K C (t) := [alog t] + , but condition (7) of [11] does not hold, whatever g > 1 may be. Hence, the existence results proved in [11] are not applicable.…”

Heteroclinic connections for fully non-linear non-autonomous second-order differential equations

“…This operator naturally arises in reaction-diffusion equations with non-constant diffusivity or in porous media equations (see [8]). Problem (P) was already considered in the framework of compact intervals in [10]. Here we investigate this problem in the whole real line and we give some general existence results (see Theorems 2 and 3) which emphasize the relevance of a precise link between the behaviors of f (t, x, ·) as y → 0 and f (·, x, y) as |t| → +∞.…”

Solvability of some boundary value problems involving p-Laplacian and non-autonomous differential operators

“…and it has been studied in many papers [1,2,7,8,12,[14][15][16]23]. We also quote [19] for systems of differential equations, [13] for differential inclusions, [17,18,24] for systems of differential inclusions. More recently, other types of differential operators, governed by an increasing function Φ, possibly singular and not necessarily surjective, have been considered.…”