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Papers by Stanislaus Maier

Communications in Partial Differential Equations, 1993

We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet... more We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet problems Lu + f(u) = 0 over bounded domains via sub- and supersolutions. A concrete example for the strictly increasing nonlinearity f is given, too.

Asymptotic Analysis, 1994

Maier, S., Non-convergent radial solutions of semilinear elliptic equations, Asymptotic Analysis ... more Maier, S., Non-convergent radial solutions of semilinear elliptic equations, Asymptotic Analysis 8 (1994) 363-377. 363 We study solutions u = u(t) of an initial value problem for u" + (n-l)/t u' + feu) = 0, which have the additional property that the limit of u as t approaches infinity does not exist. Besides some examples, we give necessary conditions on the non-linearity f for the existence of such (non-convergent) solutions. One corollary of these investigations will be that, if f(u)u >0 for small lui '# 0 then every solution u(.;p) (with Ipl small enough) of the initial value problem (1.1), stated below, converges to zero as t-+ 00.

Journal of Differential Equations, 1994

Archive for Rational Mechanics and Analysis, 1994

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.

Archive for Rational Mechanics and Analysis, 1994

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.

Asymptotic Analysis

Page 1. Asymptotic Analysis 70 (2010) 1–11 1 DOI 10.3233/ASY-2010-0998 IOS Press Nonconvergent ra... more Page 1. Asymptotic Analysis 70 (2010) 1–11 1 DOI 10.3233/ASY-2010-0998 IOS Press Nonconvergent radial solutions of semilinear elliptic equations Man Kam Kwong and Solomon Wai-Him Wong Department of Applied Mathematics ...

Communications in Partial Differential Equations, 1993

We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet... more We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet problems Lu + f(u) = 0 over bounded domains via sub- and supersolutions. A concrete example for the strictly increasing nonlinearity f is given, too.

Http Dx Doi Org 10 1080 03605309308820971, May 14, 2007

ABSTRACT

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.

Communications in Partial Differential Equations, 1993

We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet... more We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet problems Lu + f(u) = 0 over bounded domains via sub- and supersolutions. A concrete example for the strictly increasing nonlinearity f is given, too.

Asymptotic Analysis, 1994

Maier, S., Non-convergent radial solutions of semilinear elliptic equations, Asymptotic Analysis ... more Maier, S., Non-convergent radial solutions of semilinear elliptic equations, Asymptotic Analysis 8 (1994) 363-377. 363 We study solutions u = u(t) of an initial value problem for u" + (n-l)/t u' + feu) = 0, which have the additional property that the limit of u as t approaches infinity does not exist. Besides some examples, we give necessary conditions on the non-linearity f for the existence of such (non-convergent) solutions. One corollary of these investigations will be that, if f(u)u >0 for small lui '# 0 then every solution u(.;p) (with Ipl small enough) of the initial value problem (1.1), stated below, converges to zero as t-+ 00.

Journal of Differential Equations, 1994

Archive for Rational Mechanics and Analysis, 1994

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.

Archive for Rational Mechanics and Analysis, 1994

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.

Asymptotic Analysis

Page 1. Asymptotic Analysis 70 (2010) 1–11 1 DOI 10.3233/ASY-2010-0998 IOS Press Nonconvergent ra... more Page 1. Asymptotic Analysis 70 (2010) 1–11 1 DOI 10.3233/ASY-2010-0998 IOS Press Nonconvergent radial solutions of semilinear elliptic equations Man Kam Kwong and Solomon Wai-Him Wong Department of Applied Mathematics ...

Communications in Partial Differential Equations, 1993

We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet... more We prove a multiplicity result for positive solutions of a class of semilinear elliptic Dirichlet problems Lu + f(u) = 0 over bounded domains via sub- and supersolutions. A concrete example for the strictly increasing nonlinearity f is given, too.

Http Dx Doi Org 10 1080 03605309308820971, May 14, 2007

ABSTRACT

We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semil... more We consider symmetry-breaking bifurcations at non-positive, radially symmetric solutions of semilinear elliptic equations on a ball with Dirichlet boundary conditions. For nonlinearities which are asymptotically affine linear, we find solutions at which the symmetry breaks. The kernel of the linearized equation at these solutions is an absolutely irreducible representation of the group O(n). For this kind of equation a transversality condition is satisfied if the perturbation of the affine linear problem is small enough. Thus we obtain, by the equivariant branching lemma, a large variety of isotropy subgroups of O(n) which occur as symmetries of the bifurcating solution branches.