A note on the existence of time periodic solution of a superlinear heat equation

Huang, Haochuan; Yin, Jingxue; Chang, Jin Woo

doi:10.1080/00036811.2018.1460818

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Preliminaries and The Main Results2

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“…Remark We give some comments about the singular curve

\frac{q}{m} = p - 1

and critical curve

\frac{q}{m} = q_{s}

for double nonlinear Equation (). If

p = 2, m = 1

, then

\frac{q}{m} = p - 1

becomes

q = 1

, and

\frac{q}{m} = q_{s}

becomes q = p s , which are the singular exponent and critical exponent respectively for Lane–Emden type equation, see previous works 11–13 If

p = 2

, then

\frac{q}{m} = p - 1

becomes

\frac{q}{m} = 1

, and

\frac{q}{m} = q_{s}

becomes

\frac{q}{m} = p_{s}

, which are the singular exponent and critical exponent respectively for porous medium equation, see our recent work 14 …”

Section: Preliminaries and The Main Resultsmentioning

confidence: 82%

See 1 more Smart Citation

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Huang

Yin

2021

Math Methods in App Sciences

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“…Remark We give some comments about the singular curve

\frac{q}{m} = p - 1

and critical curve

\frac{q}{m} = q_{s}

for double nonlinear Equation (). If

p = 2, m = 1

, then

\frac{q}{m} = p - 1

becomes

q = 1

, and

\frac{q}{m} = q_{s}

becomes q = p s , which are the singular exponent and critical exponent respectively for Lane–Emden type equation, see previous works 11–13 If

p = 2

, then

\frac{q}{m} = p - 1

becomes

\frac{q}{m} = 1

, and

\frac{q}{m} = q_{s}

becomes

\frac{q}{m} = p_{s}

, which are the singular exponent and critical exponent respectively for porous medium equation, see our recent work 14 …”

Section: Preliminaries and The Main Resultsmentioning

confidence: 82%

“…If

p = 2, m = 1

, then

\frac{q}{m} = p - 1

becomes

q = 1

, and

\frac{q}{m} = q_{s}

becomes q = p s , which are the singular exponent and critical exponent respectively for Lane–Emden type equation, see previous works 11–13 …”

Section: Preliminaries and The Main Resultsmentioning

confidence: 96%

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Huang

Yin

2021

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

Huang

Yin

2019

Applied Mathematics and Computation

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A note on the existence of time periodic solution of a superlinear heat equation

Cited by 2 publications

References 9 publications

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

Singular curve and critical curve for doubly nonlinear Lane–Emden type equations

The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

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