Infinity of Subharmonics for Asymmetric Duffing Equations with the Lazer–Leach–Dancer Condition

Infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities

*Correspondence: [email protected] 2School of Mathematical Sciences, Soochow University, Suzhou, 215006, China Full list of author information is available at the end of the article Abstract The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic...

Semilinear Equations in R N Without Condition at Infinity

In this paper we establish that some nonlinear elliptic (and parabolic) problems are well posed in all of R N without prescribing the behavior at infinity. A typical example is the following: Let 1 < p < oo. For every f ~ Laloc(R N) there is a unique u ~ L~o~(R N) satisfying Au + lulP-Xu = f ( x ) on R N.

Boundedness of solutions for semilinear duffing equations

Duffing equations with cubic and quintic nonlinearities

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

Boundedness for Semilinear Duffing Equations at Resonance

In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.