Abstract
This paper investigates the singular Dirichlet problem
–𝑢″ = 𝑓(𝑡, 𝑢, 𝑢′), 𝑢(0) = 0, 𝑢(𝑇) = 0,
where 𝑓 satisfies the Carathéodory conditions on the set and .
The function 𝑓(𝑡, 𝑥, 𝑦) can have time singularities at 𝑡 = 0 and 𝑡 = 𝑇 and space singularities at 𝑥 = 0 and 𝑦 = 0. The existence principle for the above problem is given and its application is presented here. The paper provides conditions which guarantee the existence of a solution which is positive on (0; T) and which has the absolutely continuous first derivative on [0, 𝑇].
We establish two general principles for fixed point theorems inD-metric spaces, and then show that several theorems inD-metric spaces follow as corollaries of these general principles.
AbstractWe prove an existence principle that would apply for elliptic problems with nonlinearity separating into a difference of derivatives of two convex functions in the case when the growth conditions are imposed only on the minuend term. We present abstract result and its application. We modify the so called dual variational method.
Singular Dirichlet Boundary Value Problem for Second Order Ode