Higher order nonlinear degenerate differential operator equations

A new family of higher order nonlinear degenerate parabolic equations

x ,whereM is a specified function and H is the quadratic first order energy functional 1 2 ∫ hx dx. The energy functional arises in many physical models, but is not universal among higher order parabolic equations. Recent investigations have motivated the study of other energy functionals, such as Hp = ∫ (hx) p/2 dx for p = 2. We undertake such a study here, proving the existence of weak soluti...

Forced oscillation of higher-order nonlinear differential equations

Some new criteria have been established for the oscillation of higher-order forced nonlinear differential equation of the form Lnx(t) + q(t)F(x(t)) = e(t) according to the smart choice of a class of new auxiliary functions. No restriction is imposed on the forcing term e(t) as those assumed in [A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. ...

Oscillation Theorems for Certain Higher Order Nonlinear Functional Differential Equations

Some new oscillation theorems for higher-order nonlinear functional differential equations of the form d n dt n a(t) d n x(t) dt n α + q(t)f x g(t) = 0, α > 0, are established.

Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations

and Applied Analysis 3 Lemma 2.1 see 8, 9 . 1 If x ∈ L1 0, 1 , ρ > σ > 0, and n ∈ N, then IIx t I x t , DtIx t Iρ−σx t , 2.4 DtIx t x t , d dtn Dtx t Dt x t . 2.5 2 If ν > 0, σ > 0, then Dttσ−1 Γ σ Γ σ − ν t σ−ν−1. 2.6 Lemma 2.2 see 8 . Assume that x ∈ L1 0, 1 and μ > 0. Then IDtx t x t c1tμ−1 c2tμ−2 · · · cntμ−n, 2.7 where ci ∈ R i 1, 2, . . . , n , n is the smallest integer greater than or eq...

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations