1,720,986 research outputs found
Existence and non existence for quasivariational systems with applications to elliptic systems
No full textIn questa nota si studia esistenza locale, non esistenza globale, prolungabilità delle soluzioni di certi sistemi quasivariazionali aventi un termine di diffusione dipendente dalla soluzione e che può essere degenere o singolare. Si forniscono poi applicazioni ai sistemi ellittici
Nonexistence of nonnegative solutions of elliptic systems of divergence type
No full textAbstractIn this paper we deal with noncoercive elliptic systems of divergence type, that include both the p-Laplacian and the mean curvature operator and whose right-hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in Filippucci (2009) [12] for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev (2001) [23] and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required
with multipower forcing terms depending on the gradient
No full textIn this paper we deal with non coercive elliptic multipower systems of divergence type, which include p-Laplacian type operators as well as mean curvature operators and whose right hand sides depend on the product of both components of the solution and on a gradient factor.
We prove that any nonnegative nontrivial entire weak solution (non necessarily radial) is constant. For nontrivial solutions we intend
that both components are nontrivial. The paper improves former results due to Clèment, Fleckinger, Mitidieri, de Thèlin and to Bidaut-Veron and Pohozaev, where no gradient terms are considered
Coercive elliptic systems with gradient terms
Full text linkIn this paper we give a classification of positive radial solutions of the following system
Higher order evolution inequalities with nonlinear convolution terms
No full textWe are concerned with the study of existence and nonexistence of weak solutions to higher order evolution inequalities with nonlinear convolution terms. We assume that the weight K(x) is a radial positive and continuous function which decreases in a neighbourhood of infinity and in the problem under consideration the nonlinearity is of the type (K*|u|^p)|u|^q, p,q>0, where * denotes the standard convolution operation. We obtain necessary conditions on and such that the above problem has solutions. Our analysis emphasizes the role played by the sign of the derivative of u respect to t of order k-1
Non--existence of nodal and one--signed solutions or nonlinear variational equations with special symmetries
No full textIn this paper we extend to a particular class of symmetric operators some non existence results of nodal solutions and of solutions of constant sign of variational problems, extendig some results obtained in a previous paper [Filipppucci, Ghiselli Ricci , Pucci (1994) Archive Rat. Mech. Anal.
Erratum: "Non-existence of entire solutions of degenerate elliptic inequalities with weights''
No full textIn this erratum we correct some misprints contained in the paper "Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights" published in the same journal
Existence of solutions for critical (p,q)-Laplacian equations in ℝN
No full textIn this paper we are mainly interested in existence properties for a class of nonlinear PDEs driven by the (p,q)-Laplace operator where the reaction combines a power-type nonlinearity at critical level with a subcritical term.
In addition, nonnegative nontrivial weights and a positive parameter lambda are included in the nonlinearity. An important role in the analysis developed is played by the two potentials. Precisely, under suitable conditions on the exponents of the nonlinearity, first a detailed proof of the tight convergence of a sequence of measures is given, then the existence of a nontrivial weak solution is obtained provided that the parameter lambda is far from 0. Our proofs use concentration compactness principles by Lions and Mountain Pass Theorem by Ambrosetti and Rabinowitz
Quasilinear elliptic problems
No full textThe aim of this poster is to present a brief overview of the most significant results obtained in the last five years by the authors above
on the quasilinear elliptic theory
Existence and nonexistence of positive radial solutions of a quasilinear Dirichlet problem with diffusion
Full text linkIn this paper existence and nonexistence results of positive radial solutions
of a Dirichlet -Laplacian problem with different weights and a diffusion
term inside the divergence of the form , with
and , positive functions satisfying natural growth
conditions, are proved. Precisely, we obtain a new critical exponent
, which extends the one relative to case with no
diffusion and it divides existence from nonexistence of positive radial
solutions. The results are obtained via several tools such as a suitable
modification of the celebrated blow up technique, Liouville type theorems, a
fixed point theorem and a Poho\v zaev-Pucci-Serrin type identity
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