Non-even least energy solutions of the Emden-Fowler equation. (English) Zbl 1248.34023

Kajikiya, Ryuji

Proc. Am. Math. Soc. 140, No. 4, 1353-1362 (2012).

The author considers non-even positive solutions of the Emden-Fowler equation \[ u''(t)+h(t)u^p=0\;\;\text{in}\;\;(-1,1),\;\;\;\;u(-1)=u(1)=0, \] where \(p>1,\;h\in L^{\infty}(-1,1),\;h(t)\) is even and \(h(t)\geq 0, \,\not \equiv 0\). They prove that if the density of the coefficient function \(h\) is thin in the interior of (-1,1) and thick on the boundary, then a least energy solution is not even.

Reviewer: Yulian An (Shanghai)

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

Emden-Fowler equation; least energy solution; non-even positive solution; variational method

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