On a class of anisotropic elliptic equations without Ambrosetti–Rabinowitz type conditions

Onp→(x)-Anisotropic Problems with Neumann Boundary Conditions

“…In fact, it is known that (F4) is much weaker than the (A-R) condition in the constant exponent case (see, for instance, [22]). We will use the mountain pass theorem with Cerami condition which is weaker than (PS) condition used, for example, in [4,6].…”

“…The elliptic problems in anisotropic form concerning the Sobolev space with variable exponents have recently attracted the attention of many mathematicians; see [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references therein. Such equations arise in connection with the equations describing electromagnetic fields and the plasma physics; see [14,15] and various applications like those in thermorheological fluids [16], elastic mechanics [17], and image restoration [18].…”

Solutions for a quasilinear elliptic p⃗(x)${\vec{p}(x)}$‐Kirchhoff type problem with weight and nonlinear Robin boundary conditions

“…Note that many works have been devoted to multiplicity results for elliptic equations with variable exponents for both isotropic and anisotropic cases. (see for example [4,5], [7,13] and the references therein).…”

An Existence Result for a Class of p(x)—Anisotropic Type Equations

“…The investigation of anisotropic problems has drawn the attention of many authors; for example, see the works presented in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein. This particular interest in the study of such problems is the basis of many applications to the modeling of wave dynamics and mechanical processes in anisotropic elastic.…”