The splitting  lemmas for nonsmooth functionals on Hilbert spaces III. The case of critical manifolds

Lu, Guangcun

doi:10.5899/2019/jnaa-00337

Cited by 2 publications

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“…We can also apply to Corollaries 4.7, 4.8, Theorem 5.12 and Corollary 5.13 to suitably chosen slices in the setting of [43] to get some corresponding results. It is better for us using this idea in concrete applications.…”

Section: Applying Corollary 44 To (Lmentioning

confidence: 99%

“…Our main aim is to study generalizations of some previous famous bifurcation theorems such as those by Krasnosel'skii [37], by Rabinowitz [59], and by Fadelll and Rabinowitz [26,27] with parameterized versions of two new splitting theorems established by the author [45] and [40,41,43] (see Appendix A) and the parameterized version of a splitting lemma by Bobylev and Burman [8] (see Appendix B). The following are our basic assumptions related to them.…”

mentioning

confidence: 99%

“…Some comparisons of our results with previous work are also given in Section 3.3. In Sections 4, 5 we shall use the parameterized versions of splitting theorems [45,40,41,43] to generalize some older bifurcation theorems. Section 4 is dedicated to some generalizations of Rabinowitz bifurcation theorem [59].…”

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confidence: 99%

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Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

Lu¹

2022

DCDS

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<p style='text-indent:20px;'>This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous bifurcation theorems for potential operators by weakening standard assumptions on the differentiability of the involved functionals, which opens up a way of bifurcation studies for quasi-linear elliptic boundary value problems.</p>

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Section: Applying Corollary 44 To (Lmentioning

confidence: 99%

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confidence: 99%

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Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

Lu¹

2022

DCDS

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

2021

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Self Cite

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This is the first part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using parameterized versions of splitting theorems in Morse theory we generalize some famous bifurcation theorems for potential operators by weakening standard assumptions on the differentiability of the involved functionals, which opens up a way of bifurcation studies for quasi-linear elliptic boundary value problems.

show abstract

The splitting lemmas for nonsmooth functionals on Hilbert spaces III. The case of critical manifolds

Cited by 2 publications

References 0 publications

Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

Parameterized splitting theorems and bifurcations for potential operators, Part I: Abstract theory

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