1,721,038 research outputs found
Coupled Klein–Gordon and Born–Infeld-type equations: looking for solitary waves
No full textThe existence of infinitely many non-trivial radially symmetric solitary waves for the nonlinear Klein–Gordon equation, coupled with a Born–Infeld-type equation, is established under general assumptions
Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition
No full textWe show the incompleteness of a usually used version of the
generalized Ambrosetti–Rabinowitz condition in superlinear problems, also used in the paper cited in the title, and we propose a complete one
Pseudorelativistic Hartree Equation with General Nonlinearity: Existence, Non-existence and Variational Identities
No full textWe prove several existence and non existence results of solitary waves for a class of nonlinear pseudo–relativistic Hartree equations with general nonlinearities. We use variational methods and some new variational identities involving the half Laplacian
The Schrödinger–Poisson System with Positive Potential
No full textWe study the existence of radially symmetric solitary waves for a nonlinear Schrödinger-Poisson system. In contrast to all previous results, we consider the presence of a positive potential, of interest in physical applications
Stability of solutions of some nonlinear damped wave equations
No full textWe consider two classes of semilinear wave equations with nonnegative damping which may be of type "on-off" or integrally positive. In both cases we give a sufficient condition for the asymptotic stability of the solutions. In the case of integrally positive damping we show that such a condition is also necessary
Corrigendum and Improvements to “Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations” and Its Consequences
No full textThis paper is a corrigendum of one hypothesis introduced in Mem. Amer. Math. Soc. 242 (2016), no. 1146, and used again in J. Differential Equations 260 (2016), pp. 1314-1371 and Adv. Nonlinear Anal. 6 (2017), pp. 61-84]. We give here the corrected proofs of the concerned results, improving most of them
Quasi uniformity for the abstract Neumann antimaximum principle and applications with a priori estimates
No full textThe generalized logistic equation with indefinite weight driven by the square root of the Laplacian
No full textWe consider an elliptic problem driven by the square root of the negative
Laplacian in the presence of a general logistic function having an indefinite
weight. We prove a bifurcation result for the associated Dirichlet problem via regularity estimates of independent interest for when the weight belongs only to certain Lebesgue spaces
Quasi uniformity for the abstract Neumann antimaximum principle and applications with a priori estimates
No full textIn this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form , provided that 0 is an eigenvalue of L with associated constant eigenfunctions. To this purpose, we introduce a new notion of "quasi"-uniform maximum principle, named k-uniform maximum principle: it holds for lambda belonging to certain neighborhoods of 0 depending on the fixed positive multiplier k > 0 which selects the good class of right-hand-sides. Our approach is based on a - estimate for some related problems. As an application, we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under Neumann boundary condition
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