Boundary value problems for systems of second-order functional differential equations
نویسنده
چکیده
Systems of second-order functional differential equations (x(t)+L(x)(t)) = F (x)(t) together with nonlinear functional boundary conditions are considered. Here L : C1([0, T ];R) → C0([0, T ];R) and F : C1([0, T ];R) → L1([0, T ];R) are continuous operators. Existence results are proved by the Leray-Schauder degree and the Borsuk antipodal theorem for α-condensing operators. Examples demonstrate the optimality of conditions.
منابع مشابه
Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....
متن کاملF-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM
We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed ...
متن کاملInitial value problems for second order hybrid fuzzy differential equations
Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملStudies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
...
متن کاملSecond order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value
In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.
متن کامل