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In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical…
In the paper, we derive an existence result for a nonlinear nonautonomous partial elliptic system on an open bounded domain with Dirichlet boundary conditions, containg fractional powers of the weak Dirichlet-Laplace operator that are meant…
In the present work we briefly explain how to adapt techniques already used in fractional and $p$-fractional Laplacian cases to obtain the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution,…
This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator,…
Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite…
We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive…
We investigated the existence of solutions for a class of Ambrosetti-Prodi type systems involving the fractional Laplacian operator and with nonlinearities reaching critical growth and interacting, in some sense, with the spectrum of the…
The Graetz problem is a convection-diffusion equation in a pipe invariant along a direction. The contribution of the present work is to propose a mathematical analysis of the Neumann, Robin and periodic boundary condition on the boundary of…
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…
In this paper we show that there exist two different critical exponents for global small data solutions to the semilinear fractional diffusive equation with Caputo fractional derivative in time. The second critical exponent appears if the…
In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-\Delta)^{\frac{1}{2}} u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ in } \mathbb{R}$, for $ a>0…
We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differential equations on unbounded spatial domains to treat equations in which the linear part has order greater than two. One important example…
In this paper, we deal with the existence and multiplicity of solutions for the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the…
By means of variational methods we investigate existence, non-existence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical…
We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain…
By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…
We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the…
In this thesis we deal with two different classes of variational problems: 1) the problem of closed curves with prescribed curvature, or $H$-loop problem; 2) the study of the nodal solutions of the fractional Brezis-Nirenberg problem. In…
This paper provides necessary and sufficient conditions of optimality for variational problems that deal with a fractional derivative with respect to another function. Fractional Euler--Lagrange equations are established for the fundamental…