On solvability of nonlinear boundary value problems for the equation $(x'+g(t,x,x'))'=f(t,x,x')$ with one-sided growth restrictions on $f$
Staněk, Svatoslav
Archivum Mathematicum, Tome 038 (2002), p. 129-148 / Harvested from Czech Digital Mathematics Library
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We consider boundary value problems for second order differential equations of the form $(x^{\prime }+g(t,x,x^{\prime }))^{\prime }=f(t,x,x^{\prime })$ with the boundary conditions $r(x(0),x^{\prime }(0),x(T)) + \varphi (x)=0$, $w(x(0),x(T),x^{\prime }(T))+ \psi (x)=0$, where $g,r,w$ are continuous functions, $f$ satisfies the local Carathéodory conditions and $\varphi , \psi $ are continuous and nondecreasing functionals. Existence results are proved by the method of lower and upper functions and applying the degree theory for $\alpha $-condensing operators.

Publié le : 2002-01-01
Classification:  34B15,  47N20 
@article{107827,
     author = {Stan\v ek, Svatoslav},
     title = {On solvability of nonlinear boundary value problems for the equation $(x'+g(t,x,x'))'=f(t,x,x')$ with one-sided growth restrictions on $f$},
     journal = {Archivum Mathematicum},
     volume = {038},
     year = {2002},
     pages = {129-148},
     zbl = {1087.34007},
     mrnumber = {1909594},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107827}
}

Staněk, Svatoslav. On solvability of nonlinear boundary value problems for the equation $(x'+g(t,x,x'))'=f(t,x,x')$ with one-sided growth restrictions on $f$. Archivum Mathematicum, Tome 038 (2002) pp. 129-148. http://gdmltest.u-ga.fr/item/107827/

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