scholarly journals Critical points of solutions to elliptic problems in planar domains

2010 ◽  
Vol 10 (1) ◽  
pp. 327-338
Author(s):  
Adriana Gómez ◽  
Jaime Arango
Keyword(s):  
Critical Points ◽  
Elliptic Problems ◽  
Planar Domains

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems with the Fractional Laplacian

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Qing-Mei Zhou ◽  
Ke-Qi Wang
Keyword(s):  
Eigenvalue Problem ◽  
Critical Points ◽  
Fractional Laplacian ◽  
Nonlinear Eigenvalue Problem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractIn this paper we consider a nonlinear eigenvalue problem driven by the fractional Laplacian. By applying a version of the three-critical-points theorem we obtain the existence of three solutions of the problem in

Multiplicity of non-radial solutions of critical elliptic problems in an annulus

2005 ◽  
Vol 135 (1) ◽  
pp. 25-37 ◽  
Author(s):  
Djairo Guedes de Figueiredo ◽  
Olímpio Hiroshi Miyagaki
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Critical Sobolev Exponent ◽  
Radial Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Sobolev Exponent ◽  
Image Position

By looking for critical points of functionals defined in some subspaces of , invariant under some subgroups of O (N), we prove the existence of many positive non-radial solutions for the following semilinear elliptic problem involving critical Sobolev exponent on an annulus, where 2* − 1 := (N + 2)/(N − 2) (N ≥ 4), the domain is an annulus and f : R+ × R+ → R is a C1 function, which is a subcritical perturbation.

scholarly journals Pairs of nontrivial solutions to concave-linear-convex type elliptic problems

2020 ◽  
pp. 2050057
Author(s):  
Pasquale Candito ◽  
Salvatore A. Marano ◽  
Kanishka Perera
Keyword(s):  
Critical Points ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Critical Group ◽  
Independent Interest ◽  
Critical Groups ◽  
Nontrivial Solutions ◽  
Local Minimizers ◽  
Homotopy Invariance ◽  
Critical Sobolev Exponents

We obtain a pair of nontrivial solutions for a class of concave-linear-convex type elliptic problems that are either critical or subcritical. The solutions we find are neither local minimizers nor of mountain pass type in general. They are higher critical points in the sense that they each have a higher critical group that is nontrivial. This fact is crucial for showing that our solutions are nontrivial. We also prove some intermediate results of independent interest on the localization and homotopy invariance of critical groups of functionals involving critical Sobolev exponents.

Bifurcation results for semilinear elliptic problems in RN

2004 ◽  
Vol 134 (1) ◽  
pp. 11-32 ◽  
Author(s):  
Marino Badiale ◽  
Alessio Pomponio
Keyword(s):  
Critical Points ◽  
Elliptic Problem ◽  
Reduction Method ◽  
Elliptic Problems ◽  
Semilinear Elliptic Problem ◽  
Finite Dimensional ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems

In this paper we obtain, for a semilinear elliptic problem in RN, families of solutions bifurcating from the bottom of the spectrum of −Δ. The problem is variational in nature and we apply a nonlinear reduction method that allows us to search for solutions as critical points of suitable functionals defined on finite-dimensional manifolds.

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