Existence result for Neumann problems with p(x)-Laplacian-like operators in generalized Sobolev spaces

Nonlocal τ(m)‐Laplacian‐like problem with logarithmic nonlinearity and without Ambrosetti–Rabinowitz condition on compact Riemannian manifolds

“…This growing interest is motivated not only by the attraction of natural phenomena such as the movement of drops, waves, and bubbles but also by their importance in various practical fields, including industrial, biomedical, pharmaceutical, and microfluidic systems. In the context of the study of capillarity phenomena, many results have been obtained; see, for example, earlier studies [1][2][3][4][5][6][7][8]. The fundamental and common assumption of these works is the Ambrosetti-Rabinowitz condition [9].…”

Existence of Weak Solutions to a Class of Nonlinear Degenerate Parabolic Equations in Weighted Sobolev Space Mohamed El Ouaarabi, Chakir Allalou and Said Melliani

“…In recent years, several models from various branches of mathematical physics, such as elastic mechanics, electrorheological fluid dynamics, and image processing, have focused on the study of partial differential equations and variational problems (see for example [7,10,20]).…”

On a new p(x)-Kirchhoff type problems with p(x)-Laplacian-like operators and Neumann boundary conditions

“…The study of differential equations and variational problems with nonlinearities and nonstandard p(x)-growth conditions or nonstandard (p(x), q(x))− growth conditions have received a lot of attention. Perhaps the impulse for this comes from the new search field that reflects a new type of physical phenomenon is a class of nonlinear problems with variable exponents (see [5,9,11,21]). The motivation for this research comes from the application of similar problems in physics to model the behavior of elasticity [26] and electrorheological fluids [24], which have the ability to modify their mechanical properties when exposed to an electric field (see [19,20,22,23]), specifically the phenomenon of capillarity, which depends solid-liquid interfacial characteristics as surface tension, contact angle, and solid surface geometry.…”