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In this present paper, we are first of all interested in some continuity and compactness results for the space ψ-fractional 핊 풜 α , β ; ψ ⁢ ( Λ ) {\mathbb{S}^{\alpha,\beta;\psi}_{\mathcal{A}}(\Lambda)} . In this sense, we investigate the existence of at least two solutions with constant signs using truncation arguments and comparison methods of a new class of fractional differential equations with m ⁢ ( ξ ) {m(\xi)} -Laplacian with double phase. [ABSTRACT FROM AUTHOR]

In this paper, we use the variational method to study some singular Steklov-type problem with variable exponents. More precisely, we use the min-max method in order to prove the existence of a solution to such a problem. [ABSTRACT FROM AUTHOR]

In this paper we prove the existence of distributional solutions to certain anisotropic nonlinear weighted elliptic equations with variable exponents, where the weight function belongs to the anisotropic Sobolev space with variable exponents and zero boundary. The functional setting involves anisotropic variable exponents Lebesgue–Sobolev spaces. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of a weak solution to a Dirichlet boundary value problem for a class of nonlinear degenerate elliptic equations in the setting of weighted Sobolev spaces. Our proof is based on the weighted Sobolev spaces theory and the Browder–Minty theorem. First, we transform the problem into an equivalent operator equation; second, we utilized the Browder–Minty theorem to prove the existence and uniqueness of a weak solution to the considered problem. [ABSTRACT FROM AUTHOR]

This paper deals with the existence and multiplicity of solutions for the p ⁢ (x) p(x) -Laplacian Robin problem without the well-known Ambrosetti–Rabinowitz type growth conditions. By means of the variational approach (with the Cerami condition), existence and multiplicity results of solutions are established under weaker conditions. [ABSTRACT FROM AUTHOR]