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Session 13. Global existence versus blowup in nonlinear parabolic systems
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Existence and regularity results to the generalized Emden-Fowler equation with irregular data |
Agnieszka Kałamajska, Institute of Mathematics, University of Warsaw, Poland
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The talk is based on joint works with Katarzyna Mazowiecka and Jan Peszek
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We deal with the generalized Emden--Fowler equation \(f''(x)+g(x)f^{-\theta}(x)=0\), where \(\theta\in {\bf R}\), \(x\in(a,b)\), \(g\) belongs to \(L^p((a,b))\).
We obtain a priori estimates for the solutions, information about their asymptotic behavior near boundary points and some existence results. As a tool
we use new nonlinear variants of first and second order Poincarè inequalities,
which are based on strongly nonlinear multiplicative inequalities obtained recently in [1].
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References- Kałamajska, A. and Peszek, J., On some nonlinear
extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear
eigenvalue problems, Asymptotic Analysis, Volume 77, Number 3-4 (2012), 169-196.
- A. Kałamajska and
K. Mazowiecka, Some regularity results to the generalized Emden--Fowler equation with irregular data, o appear in Mathematical Methods
in the Applied Sciences.
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