TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions JF - Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 37-56 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we carry on the study of asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions, started in the first paper. Here we are mainly interested in the analysis of the location and shape of least energy solutions when the singular perturbation parameter tends to zero. We show that in many cases they coincide with the new solutions produced in. UR - http://hdl.handle.net/1963/3409 U1 - 926 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Concentration of solutions for some singularly perturbed mixed problems. Part I: existence results JF - Arch. Ration. Mech. Anal. 196 (2010) 907-950 Y1 - 2010 A1 - Jesus Garcia Azorero A1 - Andrea Malchiodi A1 - Luigi Montoro A1 - Ireneo Peral AB - In this paper we study the asymptotic behavior of some solutions to a singularly perturbed problem with mixed Dirichlet and Neumann boundary conditions. We prove that, under suitable geometric conditions on the boundary of the domain, there exist solutions which approach the intersection of the Neumann and the Dirichlet parts as the singular perturbation parameter tends to zero. UR - http://hdl.handle.net/1963/3406 U1 - 927 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Elliptic variational problems in $ R\\\\sp N$ with critical growth JF - J. Differential Equations 168 (2000), no. 1, 10--32 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1258 U1 - 3197 ER - TY - JOUR T1 - Existence and multiplicity results for some nonlinear elliptic equations: a survey. JF - Rend. Mat. Appl., 2000, 20, 167 Y1 - 2000 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral PB - SISSA Library UR - http://hdl.handle.net/1963/1462 U1 - 3078 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Perturbation of $\Delta u+u^(N+2)/(N-2)=0$, the scalar curvature problem in $R^N$, and related topics JF - J. Funct. Anal. 165 (1999) 117-149 Y1 - 1999 A1 - Antonio Ambrosetti A1 - Jesus Garcia Azorero A1 - Ireneo Peral AB -

Some nonlinear elliptic equations on $R^N$ which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature problem in $R^N$ are given.

PB - Elsevier UR - http://hdl.handle.net/1963/3255 U1 - 1446 U2 - Mathematics U3 - Functional Analysis and Applications ER -