Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations
In this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x...
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MDPI AG
2021-12-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3260 |
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| author | Daniela Marian |
| author_facet | Daniela Marian |
| author_sort | Daniela Marian |
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| description | In this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mo>′</mo></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><mi>x</mi><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mi>f</mi><mfenced open="(" close=")"><mi>t</mi></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mrow><mo>″</mo></mrow></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><msup><mi>x</mi><mo>′</mo></msup><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mi>f</mi><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>,</mo><mspace width="1.em"></mspace><mi>x</mi><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>=</mo><mn>0</mn><mspace width="1.em"></mspace><mi>if</mi><mspace width="1.em"></mspace><mi>t</mi><mo>≤</mo><mn>0</mn><mo>,</mo></mrow></semantics></math></inline-formula> using the Laplace transform. Our results complete those obtained by S. M. Jung and J. Brzdek for the equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mo>′</mo></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><mi>x</mi><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T03:37:41Z |
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| language | English |
| last_indexed | 2024-03-10T03:37:41Z |
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| spelling | doaj.art-f452cd126081466f90fbed586645d8292023-11-23T09:26:32ZengMDPI AGMathematics2227-73902021-12-01924326010.3390/math9243260Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential EquationsDaniela Marian0Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, RomaniaIn this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mo>′</mo></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><mi>x</mi><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mi>f</mi><mfenced open="(" close=")"><mi>t</mi></mfenced></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mrow><mo>″</mo></mrow></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><msup><mi>x</mi><mo>′</mo></msup><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mi>f</mi><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>,</mo><mspace width="1.em"></mspace><mi>x</mi><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>=</mo><mn>0</mn><mspace width="1.em"></mspace><mi>if</mi><mspace width="1.em"></mspace><mi>t</mi><mo>≤</mo><mn>0</mn><mo>,</mo></mrow></semantics></math></inline-formula> using the Laplace transform. Our results complete those obtained by S. M. Jung and J. Brzdek for the equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mo>′</mo></msup><mfenced open="(" close=")"><mi>t</mi></mfenced><mo>+</mo><mi>x</mi><mfenced separators="" open="(" close=")"><mi>t</mi><mo>−</mo><mn>1</mn></mfenced><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2227-7390/9/24/3260semi-Hyers–Ulam–Rassias stabilitydelay differential equationsLaplace transform |
| spellingShingle | Daniela Marian Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations Mathematics semi-Hyers–Ulam–Rassias stability delay differential equations Laplace transform |
| title | Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations |
| title_full | Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations |
| title_fullStr | Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations |
| title_full_unstemmed | Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations |
| title_short | Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations |
| title_sort | laplace transform and semi hyers ulam rassias stability of some delay differential equations |
| topic | semi-Hyers–Ulam–Rassias stability delay differential equations Laplace transform |
| url | https://www.mdpi.com/2227-7390/9/24/3260 |
| work_keys_str_mv | AT danielamarian laplacetransformandsemihyersulamrassiasstabilityofsomedelaydifferentialequations |