1,720,972 research outputs found
Soliton dynamics for a general class of Schrodinger equations
No full textThe soliton dynamics for a general class of nonlinear focusing Schrödinger problems in
presence of non-constant external (local and nonlocal) potentials is studied by taking as
initial datum the ground state solution of an associated autonomous elliptic equatio
Semilinear elliptic variational inequalities with dependence on the gradient via Mountain Pass techniques
No full textIn this paper we consider a semilinear variational inequality with a gradient-dependent nonlinear term. Obviously the nature of this problem is non-variational. Nevertheless we study that problem associating a suitable semilinear variational inequality, variational in nature, with it, and performing an iterative technique used in De Figueiredo et al. (2004) [6] in order to treat semilinear elliptic equations when there is a gradient dependence on the nonlinearity. We prove the existence of a non-trivial non-negative weak solution u for our problem using essentially variational methods, a penalization technique and an iterative scheme. Via Lewy-Stampacchia's estimates and regularity theory for elliptic equation we also show that u is differentiable and its gradient is alpha-Holder continuous on (Omega) over bar for any alpha is an element of (0, 1). (C) 2010 Elsevier Ltd. All rights reserved
Stability for semilinear elliptic variational inequalities depending on the gradient
No full textIn this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variational inequalities (P(n)) with a nonlinear term depending on the gradient of the solution. This paper can be seen as the second part of the work Matzeu and Servadei (2010) [9], in the sense that here we give a stability result for the C(1,alpha)-weak solutions of problem (P(n)) found in Matzeu and Servadei (2010) [9] through variational techniques. To be precise, we show that the solutions of (P(n)), found with the arguments of Matzeu and Servadei (2010) [9], converge to a solution of the limiting problem (P), under suitable convergence assumptions on the data. (C) 2011 Elsevier Ltd. All rights reserved
A linking type method to solve a class of semilinear elliptic variational inequalities
Full text linkThe aim of this paper is to study the existence of a nontrivial solution of a semilinear elliptic variational inequality with a nonlinear term satisfying superlinearity growth conditions at zero and at infinity
On Variational Inequalities Driven by Elliptic Operators Not in Divergence Form
No full textIn this paper we study semilinear variational inequalities driven by an elliptic operator not in divergence form in a bounded domain with smooth boundary. Even if this problem is not variational in nature, we will prove the existence of non-trivial non-negative solutions for it, performing a variational approach combined with a penalization technique. This kind of approach seems to be new for problems of this type. We also prove a regularity result for the solutions of our problem
Morse index for solutions of the nonlinear Schrodinger equation in a degenerate setting
No full textIn this paper, we study the Morse index of the single-peak solutions concentrating at a point of a nonlinear Schrodinger equation in a degenerate setting
Supercritical fractional Kirchhoff type problems
No full textNel lavoro si considera un problema di Kirchhoff frazionario, in presenza di un termine sopracritico. Utilizzando metodi variazionali, tecniche di troncamento e il processo iterativo di Moser, si provano due risultati di esistenza di soluzioni non banali per il problema dato, sotto due diverse ipotesi sulla funzione di Kirchhoff
A stability result for Mountain Pass type solutions of semilinear elliptic variational inequalities
No full textThe aim of the present paper is to establish a stability result for the so called Mountain Pass type solutions of a class of
semilinear elliptic variational inequalities with superlinear and subcritical nonlinearities
Variational methods for nonlocal fractional problems
No full textA thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators
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