Salvatore Angelo Marano

The existence of solutions that are positive, pointwise decaying at infinity, and weak to a fractional p-Laplacian problem in the whole space and exhibit a singular reaction is established. Truncation arguments, variational methods, as well as suitable a priori estimates are exploited.

In this paper, the existence of positive strong solutions to a Dirichlet [ ]-Laplacian problem with reaction both singular at zero and highly discontinuous is investigated. In particular, it is only required that the set of discontinuity points has Lebesgue measure zero.

In this work, the existence of solutions (in a suitable sense) to a family of inclusion systems involving fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is established. The technical approach exploits Galerkin's method and a surjective results for multifunctions in finite dimensional spaces as well as approximating techniques.

In this paper, a new framework for studying the existence of generalized or strongly generalized solutions to a wide class of inclusion systems involving double-phase, possibly competing differential operators, convection, and mixed boundary conditions is introduced. The technical approach exploits Galerkin's method and a surjective theorem for multifunctions in finite dimensional spaces.

The existence of solutions to a family of inclusion systems with fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is established. The proof uses Galerkin's method, a surjectivity result for multifunctions in finite dimensional spaces, and approximation techniques.

In this paper, the existence of positive weak solutions to a Dirichlet problem driven by the fractional $(p,q)$-Laplacian and with reaction both weakly singular and non-locally convective (i.e., depending on the distributional Riesz gradient of solutions) is established. Due to the nature of the right-hand side, we address the problem via sub-super solution methods, combined with variational techniques, truncation arguments, as well as fixed point results.

In this paper, the existence of weak solutions to some Dirichlet problems with fractional competing operators and distributional Riesz fractional gradient is investigated. Due to the nature of driving operators, the most known techniques, basically based on ellipticity and monotonicity, are no longer applicable. Generalized solutions (in a suitable sense) are obtained via an approximation procedure and a corollary of the Brouwer fixed point theorem.

In this paper, we consider a quasi-linear Dirichlet system with possible competing $(p,q)$-Laplacians and convections. Due to the lack of ellipticity, monotonicity, and variational structure, the standard approaches to the existence of weak solutions cannot be adopted. Nevertheless, through an approximation procedure and a corollary of Brouwer's fixed point theorem we show that the problem admits a solution in a suitable sense.