arXiv subjects
Publications and source records attributed to Dionicio Pastor Dallos Santos.
In this paper we study the existence of solutions for a new class of nonlinear differential equations with three-point boundary conditions. Existence of solutions are obtained by using the Leray-Schauder degree.
Using Leray-Schauder degree or degree for $α$-condensing maps we obtain the existence of at least one solution for the boundary value problem of the type \[ \left\{\begin{array}{lll} (φ(u' ))' = f(t,u,u') & & \\ u(T)=0=u'(0), & & \quad \quad \end{array}\right. \] where $φ: X\rightarrow X $ is a homeomorphism with reverse Lipschitz such that $φ(0)=0$, $f:\left[0, T\right]\times X \times X \rightarrow X $ is a continuous function, $T$ a positive real number and $X$ is a real Banach space.
In this paper we study the existence of solutions for nonlinear boundary value problems (ϕ(u' ))' = f(t,u,u'), l(u,u')=0 where l(u,u') =0 denotes the Dirichlet or mixed conditions on [0, T], ϕ is a bounded, singular or classic homeomorphism such that ϕ(0)=0, f(t,x,y) is a continuous function, and T a positive real number. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree are used.
Using Leray-Schauder degree theory we study the existence of at least one solution for the boundary value problem of the type (φ(u' ))' = f(t,u,u'), u'(0)=u(0), u'(T)= bu'(0), where φis a homeomorphism such that φ(0)=0, f is a continuous function, and T a positive real number and b some non zero real number.