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...

In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...

We consider the nonlinear Neumann problem for fully elliptic PDEs on a quadrant. establish comparison theorem viscosity sub- and supersolutions of problem. The crucial argument in proof is to build $C^{1,1}$ test function which takes care boundary condition. A similar has been treated general $n$-dimensional orthant by Biswas et al. [SIAM J. Control Optim., 55 (2017), pp. 365--396], where funct...

Convex Nonlinear Programming problems are all alike; every nonconvex problem is difficult in its own way. I am not the first numerical analyst to borrow the most quoted line of Anna Karenina to highlight the difficulties of non-linearity or non-convexity1. It could be argued that convex problems are not really “all alike”, but happy families are not either, therefore both the famous first sente...

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

There are many interesting and challenging problems in the area of classical eld theories. This area has attracted the attention of algebraists, geometers, and topol-ogists in the past and has begun to attract more analysts. Analytically, the area ooers all types of diierential equation problems which come from the two basic sets of equations in physics describing fundamental interactions, name...