Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds

Multiplicity of solutions for a fourth order elliptic equation with critical exponent on compact manifolds

This work deals with a perturbation of the so called prescribed scalar Q-curvature type equations on compact Riemannian manifolds; these equations are fourth order elliptic and of critical Sobolev growth. Sufficient conditions are given for having at least two distinct solutions. c © 2006 Elsevier Ltd. All rights reserved.

Logarithmic Bounds on Sobolev Norms for Time Dependent Linear Schrödinger Equations

Existence and mutiplicity of solutions to elliptic equations of fourth order on compact manifolds

Existence and mutiplicity of solutions to elliptic equations of fourth order on compact manifolds. Abstract. This paper deals with a fourth order elliptic equation on compact Riemannian manifolds.We establish the existence of solutions to the equation with critical Sobolev growth which is the subject of the first theorem. In the second one, we prove the multiplicity of solutions in the subcriti...

the International Congress of Chinese Mathematicians Fine Analysis of

Blow up analysis has been very useful in the study of nonlinear partial diier-ential equations. Usually blow up analysis is done with respect to energy norms, namely, giving asymptotic description in Sobolev norms to a sequence of solutions (or approximate solutions) of nonlinear partial diierential equations. In a number of applications, pointwise asymptotic analysis is needed. This is a ner b...

On the optimization of Dombi non-linear programming

Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem in which the constraints are defined as fuzzy relational equations (FRE) with the Dombi...