2008
DOI: 10.1007/s11464-008-0014-0
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Sign-changing solutions of nonlinear elliptic equations

Abstract: In this survey article, we recall some known results on existence and multiplicity of sign-changing solutions of elliptic equations. Methods for obtaining sign-changing solutions developed in the last two decades will also be briefly revisited.

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Cited by 29 publications
(10 citation statements)
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“…Over the years, combining minimax methods, the method of invariant sets of descending flow has been a powerful tool in finding sign-changing solutions of elliptic problems. For more progress in this aspect, we refer to [3,4,34,35,45] and the references therein.…”
Section: Resultsmentioning
confidence: 99%
“…Over the years, combining minimax methods, the method of invariant sets of descending flow has been a powerful tool in finding sign-changing solutions of elliptic problems. For more progress in this aspect, we refer to [3,4,34,35,45] and the references therein.…”
Section: Resultsmentioning
confidence: 99%
“…Then in the setting of Theorem 4 we obtain one positive, one negative and one sign-changing solutions. If the nonlinearity is odd in u we also obtain infinitely many sign-changing solutions by a standard argument, see [8,9,10,20,23,31].…”
Section: Lemma 6 In (35) We Have (A) H(y)mentioning
confidence: 96%
“…This requires the methods of invariant sets with gradient flows as used in [9](see [23] for more references therein). Let P ± = {u ∈ H | ± u ≥ 0} and…”
Section: Lemma 6 In (35) We Have (A) H(y)mentioning
confidence: 99%
“…In addition, the interest in problems of the existence of nodal solutions of nonlinear elliptic equations [9][10][11][12] has recently been growing. This is caused by the fact that nodal solutions arise in applications [12].…”
Section: Introductionmentioning
confidence: 99%
“…This is caused by the fact that nodal solutions arise in applications [12]. Moreover, the interest in the study of nodal solutions is related to a number of well-known unsolved problems of nonlinear analysis, such as determining the number of nodal domains and geometric properties of nodal sets of solutions [13], the problem of the generalization of the Courant theorem on zeros of eigenfunctions to nonlinear problems [14,Chap.…”
Section: Introductionmentioning
confidence: 99%