We consider the following nonlinear Schrödinger equation of derivative type: 1 $$\begin{aligned} i \partial _t u + _x^2 +i |u|^{2} _x +b|u|^4u=0 , \quad (t,x) \in {{\mathbb {R}}}\times {R}}}, \ b {R}}}. \end{aligned}$$ If $$b=0$$ this is a gauge equivalent form well-known (DNLS) equation. The soliton profile DNLS satisfies certain double power elliptic with cubic–quintic nonlinearities. quintic...

Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ...

We propose a notion of smoothness of nonexpected utility functions, which extends the variational analysis of nonexpected utility functions to more general settings. In particular, our theory applies to state dependent utilities, as well as the multiple prior expected utility model, both of which are not possible in previous literatures. Other nonexpected utility models are shown to satisfy smo...

Abstract In this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using concept of weak minima. Multiobjective find their applications in economic planning, flight control design, industrial process control, space structures, production inventory, advertising investment, impu...

The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which composed nonlinear equation with Atangana-Baleanu derivative and time-dependent inequality. We explore an existence uniqueness theorem for the under consideration. Our proof based on F-KKM theorem, Banach fixed point principle, theory monotone operators.

With the help of a new fractal derivative, model for variable coefficients and highly non-linear Schr?dinger equations on non-smooth boundary are acquired. The variational principles built successfully by coupling semi-inverse He?s two-scale transformation methods, which helpful to reveal symmetry, discover conserved quantity, obtained have widespread applications in numerical simulation.

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.

This paper aims to study a degenerate parabolic problem for solenoidal vector field in which the time derivative acts on moving body. We propose fully-discrete finite element scheme combined with backward Euler’s method saddle-point variational formulation. The convergence of this numerical is proved and error estimates some stable pairs are also established.

In this work we study variational problems, where ordinary derivatives are replaced by a generalized proportional fractional derivative. This operator depends on fixed parameter, acting as weight over the state function and its first-order We consider problem with without boundary conditions, additional restrictions like isoperimetric holonomic. Herglotz’s when in presence of time delays also c...

In this article, we discuss the numerical analysis for finite difference scheme of one-dimensional nonlinear wave equations with dynamic boundary conditions. From viewpoint discrete variational derivative method propose derivation energy-conserving schemes problem, which covers a variety as widely possible. Next, focus our attention on semilinear equation, and show existence uniqueness solution...