Geodesic
Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem
Applications of Mathematics, Tome 58 (2013) no. 1, pp. 93-110.

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

We consider the classical nonlinear fourth-order two-point boundary value problem $$ \begin {cases} u^{(4)}(t)=\lambda h(t)f(t,u(t),u'(t),u''(t)),\quad 01,\\ u(0)=u'(1)=u''(0)=u'''(1)=0. \end {cases} $$ In this problem, the nonlinear term $h(t)f(t,u(t),u'(t),u''(t))$ contains the first and second derivatives of the unknown function, and the function $h(t)f(t,x,y,z)$ may be singular at $t=0$, $t=1$ and at $x=0$, $y=0$, $z=0$. By introducing suitable height functions and applying the fixed point theorem on the cone, we establish several local existence theorems on positive solutions and obtain the corresponding eigenvalue intervals.
DOI : 10.1007/s10492-013-0004-8
Classification : 34B08, 34B09, 34B15, 34B16, 34B18, 34B27, 34L15, 47N20
Keywords: nonlinear ordinary differential equation; singular nonlinearity; positive solution; eigenvalue interval 
@article{10_1007_s10492_013_0004_8,
     author = {Yao, Qingliu},
     title = {Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem},
     journal = {Applications of Mathematics},
     pages = {93--110},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {2013},
     doi = {10.1007/s10492-013-0004-8},
     mrnumber = {3022770},
     zbl = {1274.34076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0004-8/}
}
TY  - JOUR
AU  - Yao, Qingliu
TI  - Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem
JO  - Applications of Mathematics
PY  - 2013
SP  - 93
EP  - 110
VL  - 58
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0004-8/
DO  - 10.1007/s10492-013-0004-8
LA  - en
ID  - 10_1007_s10492_013_0004_8
ER  - 
%0 Journal Article
%A Yao, Qingliu
%T Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem
%J Applications of Mathematics
%D 2013
%P 93-110
%V 58
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0004-8/
%R 10.1007/s10492-013-0004-8
%G en
%F 10_1007_s10492_013_0004_8
Yao, Qingliu. Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem. Applications of Mathematics, Tome 58 (2013) no. 1, pp. 93-110. doi : 10.1007/s10492-013-0004-8. http://geodesic.mathdoc.fr/articles/10.1007/s10492-013-0004-8/

Cité par Sources :