in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

Today due to increasing development and importance of petroleum activities andmarine transport as well as due to the mining of seabed, building activities such as construction of docks, platforms and structures as those in coastal areas and oceans has increased significantly. Concrete strength as one of the most important necessary parameters for designing, depends on many factors such as mixtu...

Water injection strings in highly deviated wells are subjected to complex forces on the string bore. In this work, a mechanical model is developed for these forces and for those on downhole tools. On the basis of this model, and taking account of the characteristics of the string in different working conditions, a temperature field model and a pressure field model are introduced, and a statical...

We give several examples of modeling in nonlinear elasticity where a quasiconvexification procedure is needed. We first recall that the three-dimensional Saint Venant-Kirchhoff energy fails to be quasiconvex and that its quasiconvex envelope can be obtained by means of careful computations. Second, we turn to the mathematical derivation of slender structure models: an asymptotic procedure using...

The diffraction of electromagnetic and light waves by an aperture in a plane conducting screen is a classical boundary value problem. As is well known, theoretical analysis aims at a solution of the vector Maxwell equations, which incorporates a prescribed form of excitation and satisfies appropriate boundary conditions on the screen and in the aperture. A small measure of progress towards this...

In this article, we study a class of Choquard–Kirchhoff type equations driven by the variable s(x,·)-order fractional p1(x,·) and p2(x,·)-Laplacian. Assuming some reasonable conditions with help variational methods, reach positive energy solution negative in an appropriate space functions. The main difficulties innovations are Choquard nonlinearities Kirchhoff functions presence double Laplace ...