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Antonio Iannizzotto

Publications and source records attributed to Antonio Iannizzotto.

At least 37 records · Page 2Linked to original sources
arXiv2019

Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian

We study a pseudo-differential equation driven by the degenerate fractional p-Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques.

math.AP↗
arXiv2019

Sobolev versus Hölder minimizers for the degenerate fractional $p$-Laplacian

We consider a nonlinear pseudo-differential equation driven by the fractional $p$-Laplacian $(-Δ)^s_p$ with $s\in(0,1)$ and $p\ge 2$ (degenerate case), under Dirichlet type conditions in a smooth domain $Ω$. We prove that local minimizers of the associated energy functional in the fractional Sobolev space $W^{s,p}_0(Ω)$ and in the weighted Hölder space $C^0_s(\overlineΩ)$, respectively, do coincide.

math.AP↗
arXiv2018

Eigenvalue problems for Fredholm operators with set-valued perturbations

By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion problem in abstract Banach spaces. Finally, we provide applications to differential inclusions.

math.AP↗
arXiv2018

Strict monotonicity and unique continuation for general non-local eigenvalue problems

We consider the weighted eigenvalue problem for a general non-local pseudo-differential operator, depending on a bounded weight function. For such problem, we prove that strict (decreasing) monotonicity of the eigenvalues with respect to the weight function is equivalent to the unique continuation property of eigenfunctions. In addition, we discuss some unique continuation results for the special case of the fractional Laplacian.

math.AP↗
arXiv2018

Fine boundary regularity for the degenerate fractional $p$-Laplacian

We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $Ω$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted Hölder regularity up to the boundary, that is, $u/d^s\in C^α(\overlineΩ)$ for some $α\in(0,1)$, $d$ being the distance from the boundary.

math.AP↗
arXiv2017

Constant sign and nodal solutions for nonhomogeneous Robin boundary value problems with asymmetric reactions

We study a nonlinear, nonhomogeneous elliptic equation with an asymmetric reaction term depending on a positive parameter, coupled with Robin boundary conditions. Under appropriate hypotheses on both the leading differential operator and the reaction, we prove that, if the parameter is small enough, the problem admits at least four nontrivial solutions: two of such solutions are positive, one is negative, and one is sign-changing. Our approach is variational, based on critical point theory, Morse theory, and truncation techniques.

math.AP↗
arXiv2017

Existence and convexity of solutions of the fractional heat equation

We prove that the initial-value problem for the fractional heat equation admits a solution provided that the (possibly unbounded) initial datum has a conveniently moderate growth at infinity. Under the same growth condition we also prove that the solution is unique. Our result does not require any sign assumption, thus complementing the Widder's type theorem of Barrios et al. (Arch. Rational Mech. Anal. 213 (2014) 629-650) for positive solutions. Finally, we show that the fractional heat flow preserves convexity of the initial datum. Incidentally, several properties of stationary convex solutions are established.

math.AP↗
arXiv2017

Existence and multiplicity results for resonant fractional boundary value problems

We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation we prove existence of a non-trivial solution. Under further assumptions on the behavior of the reaction at zero, we detect at least three non-trivial solutions (one positive, one negative, and one of undetermined sign). All results are based on the properties of weighted fractional eigenvalues, and on Morse theory.

math.AP↗
arXiv2016

Three nontrivial solutions for nonlinear fractional Laplacian equations

We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three nonzero solutions. When the reaction term is sublinear at infinity, we apply the second deformation theorem and spectral theory. When the reaction term is superlinear at infinity, we apply the mountain pass theorem and Morse theory.

math.AP↗
arXiv2015

Global Hölder regularity for the fractional $p$-Laplacian

By virtue of barrier arguments we prove $C^α$-regularity up to the boundary for the weak solutions of a non-local nonlinear problem driven by the fractional $p$-Laplacian operator. The equation is boundedly inhomogeneous and the boundary conditions are of Dirichlet type. We employ different methods according to the singular ($p<2$) of degenerate ($p>2$) case.

math.AP↗
arXiv2015

On ordinary differential inclusions with mixed boundary conditions

By means of nonsmooth critical point theory, we prove existence of three weak solutions for an ordinary differential inclusion of Sturm-Liouville type involving a general set-valued reaction term depending on a parameter, and coupled with mixed boundary conditions. As an application, we give a multiplicity result for ordinary differential equations involving discontinuous nonlinearities.

math.AP↗
arXiv2014

Three solutions for a Neumann partial differential inclusion via nonsmooth Morse theory

We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the other negative). Then, by applying the nonsmooth Morse relation, we find a third non-zero solution.

math.AP↗
arXiv2014

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.

math.AP↗
arXiv2014

Existence results for fractional p-Laplacian problems via Morse theory

We investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population dynamics and game theory. Under different growth assumptions on the reaction term, we obtain various existence as well as finite multiplicity results by means of variational and topological methods and, in particular, arguments from Morse theory.

math.AP↗
arXiv2014

Ground states for scalar field equations with anisotropic nonlocal nonlinearities

We consider a class of scalar field equations with anisotropic nonlocal nonlinearities. We obtain a suitable extension of the well-known compactness lemma of Benci and Cerami to this variable exponent setting, and use it to prove that the Palais-Smale condition holds at all level below a certain threshold. We deduce the existence of a ground state when the variable exponent slowly approaches the limit at infinity from below.

math.AP↗