in this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. these problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive banach space. to make the nonlinear methods work, some careful analysis of t...

The theory of anti-selfdual (ASD) Lagrangians developed in [8] allows a variational resolution for equations of the form Λu+Au+∂φ(u)+f = 0 where φ is a convex lower-semi-continuous function on a reflexive Banach space X, f ∈ X∗, A : D(A) ⊂ X → X∗ is a positive linear operator and where Λ : D(Λ) ⊂ X → X∗ is a non-linear operator that satisfies suitable continuity and anti-symmetry properties. AS...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

A fractal modification of the reaction-diffusion process is proposed with derivatives, and a variational principle established in space. The concentration substrate can be determined according to minimal value formulation. solution illustrated step by for ease applications engineering, effect dimensions on morphology elucidated graphically.