5 research outputs found
A note on a class of problems for a higher-order fully nonlinear equation under one-sided Nagumo-type condition
The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation
uā½āæā¾(t)=f(t,u(t),uā²(t),ā¦,uā½āæā»Ā¹ā¾(t)), nā„2,
with the boundary conditions
u^{(i)}(a) = A, for i=0,āÆ,n-3, uā½āæā»Ā¹ā¾(a) = B, uā½āæā»Ā¹ā¾(b)=C
or
u^{(i)}(a)=A, for i=0,āÆ,n-3,
cāuā½āæā»Ā²ā¾(a)-cāuā½āæā»Ā¹ā¾(a)=B,
cāuā½āæā»Ā²ā¾(b)+cāuā½āæā»Ā¹ā¾(b)=C,
with A_{i},B,CāR, for i=0,āÆ,n-3, and cā, cā, cā, cā real positive constants.
It is assumed that f:[a,b]ĆRāæā»Ā¹āR is a continuous function satisfying one-sided Nagumo-type conditions which allows an asymmetric unbounded behavior on the nonlinearity. The arguments are based on Leray-Schauder topological degree and lower and upper solutions method
Solvability of some third order boundary value problem with asymmetric unbounded nonlinearities
The purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation
uā½āæā¾(t)=f(t,u(t),uā²(t),ā¦,uā½āæā»Ā¹ā¾(t)), nā„2, with the boundary conditions
u^{(i)}(a) = A_{i}, for i=0,āÆ,n-3,
uā½āæā»Ā¹ā¾(a) = B, uā½āæā»Ā¹ā¾(b)=C
or
u^{(i)}(a)=A_{i}, for i=0,āÆ,n-3,
cāuā½āæā»Ā²ā¾(a)-cāuā½āæā»Ā¹ā¾(a)=B,
cāuā½āæā»Ā²ā¾(b)+cāuā½āæā»Ā¹ā¾(b)=C,
with A_{i},B,C ā R, for i=0,āÆ,n-3, and cā, cā, cā, cā real positive constants.
It is assumed that f:[a,b]ĆRāæā»Ā¹āR is a continuous function satisfying one-sided Nagumo-type conditions which allows an asymmetric unbounded behaviour on the nonlinearity. The arguments are based on Leray-Schauder topological degree and lower and upper solutions method
A third order boundary value problem with one-sided Nagumo condition
In this paper we present an existence and location result for the third order separated boundary value problem composed by the differential equation
uā²ā²ā²(t)=f(t,u(t),uā²(t),uā²ā²(t))
with the boundary conditons u(a)=A, uā²ā²(a)=0 and uā²ā²(b)=0, where f:[a,b]ĆRĀ³āR is a continuous funtion and AāR.
One-sided Nagumo condition, lower and upper solutions, a priori estimates and Leray-Schauder degree play an important role in the arguments
Existence result for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control
In this work we provide an existence and location result for the third order nonlinear differential equation
uā²ā²ā²(t)=f(t,u(t),uā²(t),uā²ā²(t))
where f:[a,b]ĆRĀ³āR is a continuous function, and two types of boundary conditions
u(a)=A, Ļ(uā²(b),uā²ā²(b))=0, uā²ā²(a)=B,
or
u(a)=A, Ļ(uā²(a),uā²ā²(a))=0, uā²ā²(b)=C,
with Ļ, Ļ:RĀ²āR continuous functions and monotonous in the second variable and A,B,CāR.
We assume that f satisfy a one-sided Nagumo-type condition which allows an asymmetric unbounded behavior on the nonlinearity. The arguments used concern Leray-Schauder degree theory and lower and upper solutions technique