Hölder continuous solutions for Sobolev type differential equations

2013 ◽  
Vol 287 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Rodrigo Ponce
Keyword(s):  
Differential Equations ◽  
Sobolev Type ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Sobolev Type Differential Equations

scholarly journals Sobolev type differential equations

1978 ◽  
Vol 4 (2) ◽  
pp. 147-155 ◽  
Author(s):  
V. Lakshmikantham ◽  
M. Lord
Keyword(s):  
Differential Equations ◽  
Sobolev Type ◽  
Sobolev Type Differential Equations

On the solvability of a nonlocal problem for the system of Sobolev-type differential equations with integral condition

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Anar T. Assanova
Keyword(s):  
Differential Equations ◽  
Hyperbolic Equations ◽  
Nonlocal Problem ◽  
Sufficient Conditions ◽  
Integral Relation ◽  
Integral Condition ◽  
Functional Parameter ◽  
Sobolev Type ◽  
Equivalent Problem ◽  
Sobolev Type Differential Equations

Abstract Sufficient conditions for the existence and uniqueness of a classical solution to a nonlocal problem for a system of Sobolev-type differential equations with integral condition are established. By introducing a new unknown function, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for the system of hyperbolic equations of second order with a functional parameter and an integral relation. We propose the algorithm for finding an approximate solution to the investigated problem and prove its convergence.

Solvability of nonlocal problems for systems of Sobolev-type differential equations with a multipoint condition

2019 ◽  
pp. 3-15 ◽  
Author(s):  
Anar Turmaganbetkyzy Assanova ◽  
◽  
Askarbek Ermekovich Imanchiyev ◽  
Zhazira Muratbekovna Kadirbayeva ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Sobolev Type ◽  
Nonlocal Problems ◽  
Sobolev Type Differential Equations

scholarly journals Continuous solutions to two iterative functional equations

2021 ◽  
Author(s):  
Karol Baron
Keyword(s):  
Probability Measure ◽  
Functional Equations ◽  
Continuous Functions ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

AbstractBased on iteration of random-valued functions we study the problem of solvability in the class of continuous and Hölder continuous functions $$\varphi $$ φ of the equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ \varphi (x)=F(x)+\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ), \end{aligned}$$ φ ( x ) = F ( x ) - ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , φ ( x ) = F ( x ) + ∫ Ω φ ( f ( x , ω ) ) P ( d ω ) , where P is a probability measure on a $$\sigma $$ σ -algebra of subsets of $$\Omega $$ Ω .

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