On the Sixth-Order Joseph–Lundgren Exponent

Harrabi, Abdellaziz; Rahal, Belgacem

doi:10.1007/s00023-016-0522-5

Cited by 19 publications

(25 citation statements)

References 33 publications

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“…The proof of the case , bears resemblance to an argument found in [5, 6, 8]. Now, we prove the case .…”

Section: Auxiliary Resultssupporting

confidence: 76%

“…The proof of the case , bears resemblance to an argument found in [5, 6, 8]. For more details, please see the proof of proposition 4 in [6] for the case , the proof of Lemma 4.2 in [5] for the case and the proof of Proposition 1.2 in [8] for the case .…”

Section: Auxiliary Resultsmentioning

confidence: 57%

“…For more details, please see the proof of proposition 4 in [6] for the case , the proof of Lemma 4.2 in [5] for the case and the proof of Proposition 1.2 in [8] for the case . For this reason, we omit the details.…”

Section: Auxiliary Resultsmentioning

confidence: 99%

“…This device allows us to avoid the spherical integrals raised in [21], which are very difficult to control, especially for the polyharmonic situations. For , the Pohozaev identity is similar to [7, 8, 20, 22]. …”

Section: Auxiliary Resultsmentioning

confidence: 99%

“…Thanks to the Liouville-type theorem with finite Morse index in [8], the authors proved the nonexistence result of sign-changing solutions for the sixth-order problem Let us give a brief sketch of their method. They proved various classification theorems and Liouville-type results for -solutions belonging to one of the following classes: stable solutions, solutions which are stable outside a compact set of .…”

Section: Introductionmentioning

confidence: 99%

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Classification of stable solutions for non-homogeneous higher-order elliptic PDEs

2017

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Under some assumptions on the nonlinearity f, we will study the nonexistence of nontrivial stable solutions or solutions which are stable outside a compact set of for the following semilinear higher-order problem: with . The main methods used are the integral estimates and the Pohozaev identity. Many classes of nonlinearity will be considered; even the sign-changing nonlinearity, which has an adequate subcritical growth at zero as for example , where , , , . More precisely, we shall revise the nonexistence theorem of Berestycki and Lions (Arch. Ration. Mech. Anal. 82:313-345, 1983) in the class of smooth finite Morse index solutions as the well known work of Bahri and Lions (Commun. Pure Appl. Math. 45:1205-1215, 1992). Also, the case when is a nonnegative function will be studied under a large subcritical growth assumption at zero, for example or , and . Extensions to solutions which are merely stable are discussed in the case of supercritical growth with .

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“…The proof of the case , bears resemblance to an argument found in [5, 6, 8]. Now, we prove the case .…”

Section: Auxiliary Resultssupporting

confidence: 76%