scholarly journals A general existence principle for strong solutions to the Dirichlet problem for the equation Δ u + f(t, u) = 0

1997 ◽  
Vol 10 (3) ◽  
pp. 29-32 ◽  
Author(s):  
D. O'Regan
Keyword(s):  
Dirichlet Problem ◽  
Strong Solutions ◽  
Existence Principle ◽  
General Existence

scholarly journals Singular Dirichlet Boundary Value Problem for Second Order Ode

2007 ◽  
Vol 14 (2) ◽  
pp. 325-340
Author(s):  
Irena Rachůnková ◽  
Jakub Stryja
Keyword(s):  
Dirichlet Problem ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Value Problem ◽  
Existence Of A Solution ◽  
Absolutely Continuous ◽  
First Derivative ◽  
Carathéodory Conditions ◽  
Time Singularities ◽  
Existence Principle ◽  
Singular Dirichlet Problem

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].

scholarly journals A general existence principle for fixed point theorems inD-metric spaces

2000 ◽  
Vol 23 (7) ◽  
pp. 441-448 ◽  
Author(s):  
B. C. Dhage ◽  
A. M. Pathan ◽  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Principle ◽  
General Existence

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.

A note on a dirichlet problem with concave-convex nonlinearity

2010 ◽  
Vol 60 (3) ◽  
Author(s):  
Marek Galewski
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Convex Functions ◽  
Elliptic Problems ◽  
Growth Conditions ◽  
Abstract Result ◽  
Dual Variational Method ◽  
Existence Principle ◽  
Derivatives Of

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.

Wω2,p -Solvability of the Cauchy–Dirichlet Problem for Nondivergence Parabolic Equations with BMO Coefficients

2012 ◽  
Vol 64 (1) ◽  
pp. 217-240 ◽  
Author(s):  
Lin Tang
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Strong Solutions ◽  
Weighted Spaces ◽  
Bmo Coefficients

AbstractIn this paper, we establish the regularity of strong solutions to nondivergence parabolic equations with BMO coefficients in nondoubling weighted spaces.

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