Existence and bifurcation results for a class of nonlinear boundary value problems in $(0,\infty )$

Rother, Wolfgang. "Existence and bifurcation results for a class of nonlinear boundary value problems in $(0,\infty )$." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 297-305. <http://eudml.org/doc/247288>.

@article{Rother1991,
abstract = {We consider the nonlinear Dirichlet problem \[ -u^\{\prime \prime \} -r(x)|u|^\sigma u= \lambda u \text\{ in \} (0,\infty ), \, u(0)=0 \text\{ and \} \lim \_\{x\rightarrow \infty \} u(x)=0, \] and develop conditions for the function $r$ such that the considered problem has a positive classical solution. Moreover, we present some results showing that $\lambda =0$ is a bifurcation point in $W^\{1,2\} (0,\infty )$ and in $L^p(0,\infty )\, (2\le p\le \infty )$.},
author = {Rother, Wolfgang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonlinear Dirichlet problem; classical solution; bifurcation point; ordinary differential equation; nonlinear Dirichlet problem; classical solution; bifurcation point; minimum of a functional},
language = {eng},
number = {2},
pages = {297-305},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence and bifurcation results for a class of nonlinear boundary value problems in $(0,\infty )$},
url = {http://eudml.org/doc/247288},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Rother, Wolfgang
TI - Existence and bifurcation results for a class of nonlinear boundary value problems in $(0,\infty )$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 297
EP - 305
AB - We consider the nonlinear Dirichlet problem \[ -u^{\prime \prime } -r(x)|u|^\sigma u= \lambda u \text{ in } (0,\infty ), \, u(0)=0 \text{ and } \lim _{x\rightarrow \infty } u(x)=0, \] and develop conditions for the function $r$ such that the considered problem has a positive classical solution. Moreover, we present some results showing that $\lambda =0$ is a bifurcation point in $W^{1,2} (0,\infty )$ and in $L^p(0,\infty )\, (2\le p\le \infty )$.
LA - eng
KW - nonlinear Dirichlet problem; classical solution; bifurcation point; ordinary differential equation; nonlinear Dirichlet problem; classical solution; bifurcation point; minimum of a functional
UR - http://eudml.org/doc/247288
ER -