186,478 research outputs found
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
Nonlinear weighted p-Laplacian elliptic inequalities with gradient terms
No full textIn this paper, we give sufficient conditions for the existence and nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p-2Du} ≥ h(|x|)f(u)l(|Du|). We achieve our conclusions by using a generalized version of the well-known Keller–Ossermann condition, first introduced in [2] for the generalized mean curvature case, and in [11, Sec. 4] for the nonweighted p-Laplacian equation. Several existence results are also proved in Secs. 2 and 3, from which we deduce simple criteria of independent interest stated in the Introduction
On weak solutions of nonlinear weighted p-Laplacian elliptic inequalities
No full textIn this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of class of p-Laplacian elliptic inequalities with possibly singular weights. In order to get the results a new Omori–Yau type principle is used. We complement our nonexistence results by establishing existence of infinitely many positive radial solutions each of which blows up at some finite R>0. Finally, a criterium for the existence of positive entire large radial solutions of class is also established
Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights
No full textNon-existence results for non-negative distribution entire solutions of singular quasilinear elliptic differential inequalities with weights are established. Such inequalities include the capillarity equation with varying gravitational field h, as well as the general p-Poisson equation of radiative cooling with varying heat conduction coefficient g and varying radiation coefficient h. Since we deal with inequalities and positive weights, it is not restrictive to assume h radially symmetric. Theorem 1 extends in several directions previous results and says that solely entire large solutions can exist, while Theorem 2 shows that in the p-Laplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest
On entire solutions of degenerate elliptic differential inequalities with nonlinear gradient terms
No full textAbstractIn this paper we give sufficient conditions for the nonexistence of nonnegative nontrivial entire weak solutions of p-Laplacian elliptic inequalities, with possibly singular weights and gradient terms, of the form div{g(|x|)|Du|p−2Du}⩾h(|x|)f(u)±h˜(|x|)ℓ(|Du|), under the main request that h and h˜ are continuous on R+. We achieve our conclusions introducing a generalized version of the well-known Keller–Osserman condition
Il “filo di Arianna”: di Toyo Ito, Kengo Kuma, Edward Suzuki e Atsushi Kitagawara.
No full textbrevi interviste a Toyo Ito, Kengo Kuma, Edward Suzuki e Atsushi Kitagawara
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
La sottile linea rossa: percorso nel linguaggio dei progetti
No full textcon 40 schede di architetture giapponesi suddivise secondo una classificazione semantica (Shizen, En, Miegakure, Mitate, Hitaisho, Heichi, Makoto, Monono Aware, Wabi-Sabi, Yohaku-Shibui, Oku, Do-Hyoshi, Takumi
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