zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the effect of critical points of distance function in superlinear elliptic problems. (English) Zbl 0989.35054
Summary: We study some perturbed semilinear problems with Dirichlet or Neumann boundary conditions, $$\cases -\varepsilon^2 \Delta u+u= u^p\quad & \text{in }\Omega\\ u>0 & \text{in }\Omega\\ u=0\text{ or }{\partial u\over \partial v}=0 & \text{in }\partial \Omega,\endcases$$ where $\Omega$ is a bounded, smooth domain of $\bbfR^N$, $N\ge 2$, $\varepsilon >0$, $1<p< {N+2\over N-2}$ if $N\ge 3$ or $p>1$ if $N=2$ and $\nu$ is the unit outward normal at the boundary of $\Omega$. We show that any “suitable” critical point $x_0$ of the distance function generates a family of single interior spike solutions, whose local maximum point tends to $x_0$ as $\varepsilon$ tends to zero.

35J65Nonlinear boundary value problems for linear elliptic equations
35B25Singular perturbations (PDE)
35J20Second order elliptic equations, variational methods