Geodesic
Solvability of a generalized third-order left focal problem at resonance in Banach spaces
Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 361-382.

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

This paper deals with the generalized nonlinear third-order left focal problem at resonance $$ \begin {cases} (p(t)u''(t))'-q(t)u(t)=f(t, u(t), u'(t), u''(t)), \quad t\in \mathopen ]t_0, T[, m(u(t_0), u''(t_0))=0, n(u(T), u'(T))=0, l(u(\xi ), u'(\xi ), u''(\xi ))=0, \end {cases} $$ where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions by using the topological degree technique as well as some recent generalizations of this technique. Our results are generalizations and extensions of the results of several authors. An application is included to illustrate the results obtained.
DOI : 10.21136/MB.2013.143510
Classification : 34B15, 47J05
Keywords: Fredholm operator; coincidence degree; left focal problem; nontrivial solution; resonance 
@article{10_21136_MB_2013_143510,
     author = {Zhang, Youwei},
     title = {Solvability of a generalized third-order left focal problem at resonance in {Banach} spaces},
     journal = {Mathematica Bohemica},
     pages = {361--382},
     publisher = {mathdoc},
     volume = {138},
     number = {4},
     year = {2013},
     doi = {10.21136/MB.2013.143510},
     mrnumber = {3231092},
     zbl = {06260038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143510/}
}
TY  - JOUR
AU  - Zhang, Youwei
TI  - Solvability of a generalized third-order left focal problem at resonance in Banach spaces
JO  - Mathematica Bohemica
PY  - 2013
SP  - 361
EP  - 382
VL  - 138
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143510/
DO  - 10.21136/MB.2013.143510
LA  - en
ID  - 10_21136_MB_2013_143510
ER  - 
%0 Journal Article
%A Zhang, Youwei
%T Solvability of a generalized third-order left focal problem at resonance in Banach spaces
%J Mathematica Bohemica
%D 2013
%P 361-382
%V 138
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143510/
%R 10.21136/MB.2013.143510
%G en
%F 10_21136_MB_2013_143510
Zhang, Youwei. Solvability of a generalized third-order left focal problem at resonance in Banach spaces. Mathematica Bohemica, Tome 138 (2013) no. 4, pp. 361-382. doi : 10.21136/MB.2013.143510. http://geodesic.mathdoc.fr/articles/10.21136/MB.2013.143510/

Cité par Sources :