Potential well method for a class of fourth order wave equations with Newtonian potential

Decay Estimates for Fourth Order Wave Equations

may be thought of as a nonlinear beam equation. In this paper we obtain both L-L estimates and space-time integrability estimates on solutions to the linear equation. We also use these estimates to study the local existence and asymptotic behavior of solutions to the nonlinear equation, for nonlinear terms which grow like a certain power of u. The main L-L estimate (Theorem 2.1) states that sol...

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

The variational iteration method for a class of tenth-order boundary value differential equations

Numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well

where 2u = ( u), N > 4, λ > 0, 1 < q < 2 and μ ∈ [0,μ0], 0 < μ0 <∞. The continuous function f verifies the assumptions: (f1) f (s) = o(|s|) as s→ 0; (f2) f (s) = o(|s|) as |s| →∞; (f3) F(u0) > 0 for some u0 > 0, where F(u) = ∫ u 0 f (t) dt. According to hypotheses (f1)–(f3), the number cf = max s =0 | f (s) s | > 0 is well defined (see [1]). The continuous functions α and K verify the assumptio...