Dual fountain theorem

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August undefined, 2024

WebMar 2, 2024 · tool to obtain this multiplicity result is the dual fountain theorem. This result of multi-ple solutions to nonlinear elliptic problems is motivated by the contributions in recent works [23,30,33–39], and the references therein. In particular, Alves–Liu [33] obtained the existence and multiplicity results to the superlinear r(x)-Laplacian ... WebIn the present paper, based on the dual fountain theorem, we can prove the same result under a more generic condition, which generalizes the result in [17]. Our first result can be stated as follows. Theorem 1.2 Assume that V satisfies (VI) V e C (R3, R) and infxeR3 V (x)> 0; and/ satisfies the/ollowing conditions.

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WebDec 6, 2013 · This critical point theorem generalizes the dual fountain theorem of Bartsch and Willem, and is not based on any reduction method. It should be noted that problem ( MathML) does not fit into the framework of the theorem proved in [ 18 ], which is only suitable for finding large energy solutions. WebProof of Theorem 10. As a consequence of Lemmas 8 and 9 and Mountain Pass theorem, we get the desired result. Proof of Theorem 11. Since is a reflexive and separable Banach space, there exist and such that in which Set We will use Dual Fountain theorem Lemma 5 to prove Theorem 2. Set is a -functional on . cultural studies thesis topics

On a -Kirchhoff equation via Fountain Theorem and Dual ... - Re…

WebFountain theorem Michel Willem Chapter 1154 Accesses Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE,volume 24) Abstract When a functional is invariant, we use a more precise version of the quantitative deformation lemma. Download chapter PDF Author information Authors and Affiliations WebDec 12, 2024 · The first one is to discuss that our problem has infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy … WebThe so-called double-well potential is one of a number of quartic potentials of considerable interest in quantum mechanics, in quantum field theory and elsewhere for the exploration … east lyme primary care

On a p-Kirchhoff equation via Fountain Theorem and Dual Fountain ...

WebThe five volumetric components of the Dual Formation Model are pictured above. Program LVPM offers modeling for two such formations. Both will generally contain instances of … WebCite this chapter. Willem, M. (1996). Fountain theorem. In: Minimax Theorems. Progress in Nonlinear Differential Equations and Their Applications, vol 24. east lyme property linesWebFeb 1, 2024 · By linking theorem with Cerami condition, the fountain theorem and dual fountain theorem with Cerami condition, we obtain some existence of weak solutions for the above equations under our considerations which are … cultural sustainability in education

"WebDec 6, 2013 · This critical point theorem generalizes the dual fountain theorem of Bartsch and Willem, and is not based on any reduction method. It should be noted that problem … " - Dual fountain theorem

Dual fountain theorem

WebMar 1, 2001 · Fountain theorems and their dual form were established by Bartsch in [3] and by Bartsch–Willem in [4] (see also [16]) respectiv ely. … WebApr 10, 2024 · Different from the previous ones which have recently appeared, we weaken the condition of $ M $ and obtain the existence and multiplicity of solutions via the symmetric mountain pass theorem and the theory of the fractional Sobolev space with variable exponents.

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WebSep 26, 1993 · Here, finally, is the explanation: One hole shoots out hydrogen. The other shoots out oxygen. The two streams come together and form H2O, water. OK, so that's a … WebFeb 17, 2024 · The primary tools to obtain such multiplicity results are the fountain theorem and the dual fountain theorem, respectively. This paper is …

WebDec 12, 2024 · The first one is to discuss that our problem has infinitely many large energy solutions. Second, we obtain the existence of a sequence of infinitely many small energy solutions to the given problem. To establish such multiplicity results, we employ the fountain theorem and the dual fountain theorem as the primary tools, respectively. WebDOUBLE DELTA FUNCTION WELL 7 FIGURE 4. Graphical solution of 38, with y=4˘in red and y= 1 e 2˘ in blue. We see there is a solution near ˘= 0:8 and using Maple, we ﬁnd ˘=

WebMar 23, 2024 · By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely … WebJan 21, 2024 · The main purpose is to show the existence of infinitely many large- or small- energy solutions to the problem above. The strategy of the proof for these results is to approach the problem variationally by employing the variational methods, namely, the fountain and the dual fountain theorem with Cerami condition.

WebBy using Ekeland’s variational principle and dual fountain theorem, we obtain some new existence and multiplicity of negative energy solutions for the above problem …

WebThe primary tools to obtain such multiplicity results are the fountain theorem and the dual fountain theorem, respectively. Such existence results of multiple solutions to nonlinear elliptic problems are particularly motivated by the contributions in recent studies [1,5,17,18,20,24,28,31,32, 34,36–38,44,46], and the references therein. cultural symbols in philippinesWebNotes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent. Opuscula Mathematica 2024 Journal article ... Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely. Studia Mathematica 2005 Journal article DOI: 10.4064/sm170-3-5 EID: cultural sweatshirtsWeb1.2 will be proved by using a new critical point theorem for strongly ﬁ , established in this pape, which can be viewed as a strongly ﬁ version of the dual fountain theorem of Bartsch and Willem [7]. T dual fountain theorem in [ 7] cannot deal with the strongly ﬁ . T working space E in [7] had the orthogonal decomposition E = ∞ j= X j ... cultural symbol of chinaWebJul 31, 2024 · Using different versions of the Mountain Pass Theorem, as well as, the Fountain Theorem and Dual Fountain Theorem with Cerami condition, we obtain the existence of weak solutions for the problem ( P λ) and we show that the problem treated has at least one nontrivial solution for any parameter λ > 0 small enough as well as that the … east lyme property tax billWebtheorem · Dual Fountain theorem Mathematics Subject Classiﬁcation 35A15 · 35D30 · 35J60 · 35J62 · 46E35 B O. H. Miyagaki [email protected] E. Juárez Hurtado [email protected] R. S. Rodrigues [email protected] 1 Department of Mathematics, Universidade Federal de São Carlos, São Carlos, SP CEP 13565-905, cultural symbols of americaWebJun 1, 2024 · Therefore, like many critical point theorems the Dual fountain theorem holds under (C) * c condition.Next lemma is due to [27, Lemma 3.2] Lemma 6.4. Suppose that the hypotheses in Theorem 1.3 hold ... cultural syndromes psychology definitionWebtheorem · Dual Fountain theorem Mathematics Subject Classiﬁcation 35A15 · 35D30 · 35J60 · 35J62 · 46E35 B O. H. Miyagaki [email protected] E. Juárez Hurtado … cultural synergy meaning