Existence Theorems for a Fourth Order Boundary Value Problem

A. El-Haffaf. "Existence Theorems for a Fourth Order Boundary Value Problem." Bulletin of the Polish Academy of Sciences. Mathematics 57.2 (2009): 135-148. <http://eudml.org/doc/286604>.

@article{A2009,
abstract = {This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $x^\{(4)\}(t) + f(t,x(t),x^\{\prime \prime \}(t)) = 0$, 0 < t < 1, x(0) = x’(0) = 0, x”(1) = 0, $x^\{(3)\}(1) = 0$. Boundary value problems of very similar type are also considered. It is assumed that f is a function from the space C([0,1]×ℝ²,ℝ). The main tool used in the proof is the Leray-Schauder nonlinear alternative.},
author = {A. El-Haffaf},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
language = {eng},
number = {2},
pages = {135-148},
title = {Existence Theorems for a Fourth Order Boundary Value Problem},
url = {http://eudml.org/doc/286604},
volume = {57},
year = {2009},
}

TY - JOUR
AU - A. El-Haffaf
TI - Existence Theorems for a Fourth Order Boundary Value Problem
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 2
SP - 135
EP - 148
AB - This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $x^{(4)}(t) + f(t,x(t),x^{\prime \prime }(t)) = 0$, 0 < t < 1, x(0) = x’(0) = 0, x”(1) = 0, $x^{(3)}(1) = 0$. Boundary value problems of very similar type are also considered. It is assumed that f is a function from the space C([0,1]×ℝ²,ℝ). The main tool used in the proof is the Leray-Schauder nonlinear alternative.
LA - eng
UR - http://eudml.org/doc/286604
ER -