Geodesic
Strong singularities in mixed boundary value problems
Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 393-409.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study singular boundary value problems with mixed boundary conditions of the form \[ (p(t)u^{\prime })^{\prime }+ p(t)f(t,u,p(t)u^{\prime })=0, \quad \lim _{t\rightarrow 0+}p(t)u^{\prime }(t)=0, \quad u(T)=0, \] where $[0,T]\subset {\mathbb{R}}.$ We assume that ${\mathbb{R}}^2,$ $f$ satisfies the Carathéodory conditions on $(0,T)\times $ $p\in C[0,T]$ and ${1/p}$ need not be integrable on $[0,T].$ Here $f$ can have time singularities at $t=0$ and/or $t=T$ and a space singularity at $x=0$. Moreover, $f$ can change its sign. Provided $f$ is nonnegative it can have even a space singularity at $y=0.$ We present conditions for the existence of solutions positive on $[0,T).$
DOI : 10.21136/MB.2006.133975
Classification : 34B15, 34B16, 34B18
Keywords: singular mixed boundary value problem; positive solution; lower function; upper function; convergence of approximate regular problems 
@article{10_21136_MB_2006_133975,
     author = {Rach\r{u}nkov\'a, Irena},
     title = {Strong singularities in mixed boundary value problems},
     journal = {Mathematica Bohemica},
     pages = {393--409},
     publisher = {mathdoc},
     volume = {131},
     number = {4},
     year = {2006},
     doi = {10.21136/MB.2006.133975},
     mrnumber = {2273930},
     zbl = {1114.34020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133975/}
}
TY  - JOUR
AU  - Rachůnková, Irena
TI  - Strong singularities in mixed boundary value problems
JO  - Mathematica Bohemica
PY  - 2006
SP  - 393
EP  - 409
VL  - 131
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133975/
DO  - 10.21136/MB.2006.133975
LA  - en
ID  - 10_21136_MB_2006_133975
ER  - 
%0 Journal Article
%A Rachůnková, Irena
%T Strong singularities in mixed boundary value problems
%J Mathematica Bohemica
%D 2006
%P 393-409
%V 131
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133975/
%R 10.21136/MB.2006.133975
%G en
%F 10_21136_MB_2006_133975
Rachůnková, Irena. Strong singularities in mixed boundary value problems. Mathematica Bohemica, Tome 131 (2006) no. 4, pp. 393-409. doi : 10.21136/MB.2006.133975. http://geodesic.mathdoc.fr/articles/10.21136/MB.2006.133975/

Cité par Sources :