12 research outputs found
A variant of Banach’s contraction principle in ordered Banach spaces
No full textIn this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative
Complete description of the set of solutions to a strongly nonlinear O.D.E's
No full textWe give a complete description of the set of solutions to the boundary value problem
where is an odd increasing homeomorphism of concave on and is odd and superlinear
Uniqueness of fixed point for sum of operators in ordered Banach spaces and application
No full textIn this article, we are concerned by existence and uniqueness of a fixed point for the sum of two operators A and B, defined on a closed convex subset of an ordered Banach space, where the order is induced by a normal and minihedral cone. In such a structure, an absolute value function is generated by the order and this provide the ability to introduce new versions of the concepts of lipschitzian and expansive mappings. Therefore we prove that if A is expansive and B is contractive, then the sum A + B has a unique fixed point
Positive solution to the nonlinear abstract hammerstein equation and applications to φ -Laplacian BVPs
No full textBoundary-value Problems for the One-dimensional p-Laplacian with Even Superlinearity
No full textThis paper is concerned with a study of the quasilinear problem
-(|u'|^{p-2}u')'= |u|^p-\lambda, in (0,1)
,
where p greater than 1 and are parameters. For positive, we determine a lower bound for the number of solutions and establish their nodal properties. For , we determine the exact number of solutions. In both cases we use a quadrature method.Mathematic
Nodal solutions for singular second-order boundary-value problems
No full textWe use a global bifurcation theorem to prove the existence of
nodal solutions to the singular second-order two-point boundary-value
problem
\displaylines{
-( pu') '(t)=f(t,u(t))\quad t\in ( \xi ,\eta) , \cr
au(\xi )-b\lim_{t\to\xi} p(t)u'(t)=0, \cr
cu(\eta )+d\lim_{t\to\eta} p(t)u'(t)=0,
}
where , are real numbers with ,
, is a measurable
function with and
is a Caratheodory
function
Fixed point theorems in the study of positive strict set-contractions
No full textThe author uses fixed point index properties and Inspired by the work in Benmezai and Boucheneb (see Theorem 3.8 in [3]) to prove new fixed point theorems for strict set-contraction defined on a Banach space and leaving invariant a con
Sturm-Liouville BVPs with Caratheodory nonlinearities
No full textIn this article we study the existence and multiplicity of solutions for
several classes of Sturm-Liouville boundary value problems having
Caratheodory nonlinearities. Many results existing in the literature for
such boundary value problems in the continuous framework will find in this
work their extensions to the Caratheodory setting
POSITIVE SOLUTIONS TO A TWO POINT SINGULAR BOUNDARY VALUE PROBLEM
No full textAbstract. We employ fixed point index theory to establish existence results for positive solutions to the singular boundary value problem where a ∈ C 1 ((0,1),(0,∞)) , 1/a is integrable on any compact subset of (0,1] , b ∈ C((0,1) , [0,+∞)) does not vanish identically and is integrable on any compact subset of [0,1) , and f : As applications, existence and nonexistence criteria for positive radial solutions to some elliptic equations are deduced
