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Applicable Analysis
An International Journal
Volume 56, 1995 - Issue 3-4
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Original Articles

On sign-changing solutions of certain semilinear elliptic problems

E.N. Dancer School of Mathematics and Statistics, The University of Sydney, Sydney, AustraliaView further author information
&
DU Yihong Department of Mathematics, Statistics and Computing Science, The University of New England, AustraliaView further author information
Pages 193-206 | Received 25 Feb 1994, Published online: 20 Jan 2011

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Rodrigo F. Gabert & Rodrigo S. Rodrigues. (2020) Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities. Complex Variables and Elliptic Equations 65:2, pages 272-292.
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M. Schechter, Z.-Q. Wang & W. Zou. (2005) New Linking Theorem and Sign-Changing Solutions. Communications in Partial Differential Equations 29:3-4, pages 471-488.
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Thomas Bartsch, Zhaoli Liu & Tobias Weth. (2005) Sign Changing Solutions of Superlinear Schrödinger Equations. Communications in Partial Differential Equations 29:1-2, pages 25-42.
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Lucas Fresse & Viorica V. Motreanu. (2023) An abstract sub-supersolution method in partially ordered spaces. Nonlinear Analysis: Real World Applications 70, pages 103784.
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F. Faraci & D. Puglisi. (2022) Nodal solutions of semi-linear elliptic equations with dependence on the gradient. Bulletin des Sciences Mathématiques 175, pages 103101.
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Antonio Iannizzotto & Roberto Livrea. (2021) Four Solutions for Fractional p-Laplacian Equations with Asymmetric Reactions. Mediterranean Journal of Mathematics 18:5.
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Xiaoyan Lin & Xianhua Tang. (2018) Ground state sign-changing solutions for semilinear Dirichlet problems. Boundary Value Problems 2018:1.
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Jian Zhang, Bitao Cheng, Xianhua Tang & Wen Zhang. (2016) Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type. Communications on Pure and Applied Analysis 15:6, pages 2161-2177.
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Michael E. Filippakis, Donal O'Regan & Nikolaos S. Papageorgiou. (2014) Multiple and nodal solutions for nonlinear equations with a nonhomogeneous differential operator and concave-convex terms. Tohoku Mathematical Journal 66:4.
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Zhitao ZhangZhitao Zhang. 2013. Variational, Topological, and Partial Order Methods with Their Applications. Variational, Topological, and Partial Order Methods with Their Applications 221 248 .
XU XIAN. (2011) SIGN-CHANGING SOLUTIONS OF ( e 1 , B )-LIMIT INCREASING OPERATOR EQUATION . Glasgow Mathematical Journal 53:3, pages 535-554.
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Tobias Weth. (2010) Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods. Jahresbericht der Deutschen Mathematiker-Vereinigung 112:3, pages 119-158.
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Leszek Gasiński & Nikolaos S. Papageorgiou. (2009) Nodal and multiple constant sign solutions for resonant -Laplacian equations with a nonsmooth potential. Nonlinear Analysis: Theory, Methods & Applications 71:11, pages 5747-5772.
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Xu Xian, Donal O’Regan & Zhang Ruifang. (2008) Existence and location results for sign-changing solutions for three-point boundary value problems using Leray-Schauder degree. Monatshefte für Mathematik 158:4, pages 413-439.
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Colette De Coster. (2009) Sign-changing solutions and multiplicity results for elliptic problems via lower and upper solutions. Nonlinear Differential Equations and Applications NoDEA 16:6, pages 745-769.
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Giuseppina Barletta & Nikolaos S. Papageorgiou. (2009) Multiple nontrivial solutions for semilinear elliptic problems. Nonlinear Analysis: Theory, Methods & Applications 71:10, pages 4321-4345.
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RaviP Agarwal, MichaelE Filippakis, Donal O'Regan & NikolaosS Papageorgiou. (2009) Constant Sign and Nodal Solutions for Problems with the -Laplacian and a Nonsmooth Potential Using Variational Techniques. Boundary Value Problems 2009:1, pages 820237.
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Michael E. Filippakis & Nikolaos S. Papageorgiou. (2008) Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian. Journal of Differential Equations 245:7, pages 1883-1922.
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Nikolaos S. Papageorgiou, Eugénio M. Rocha & Vasile Staicu. (2008) Multiplicity theorems for superlinear elliptic problems. Calculus of Variations and Partial Differential Equations 33:2, pages 199-230.
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Xian Xu & Donal O’Regan. (2008) Multiplicity of sign-changing solutions for some four-point boundary value problem. Nonlinear Analysis: Theory, Methods & Applications 69:2, pages 434-447.
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Zhaoli Liu & Zhi-Qiang Wang. (2008) Sign-changing solutions of nonlinear elliptic equations. Frontiers of Mathematics in China 3:2, pages 221-238.
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Zhi-Qiang Wang & Zhaoli Liu. (2005) Multi-bump type nodal solutions having a prescribed number of nodal domains: I. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 22:5, pages 597-608.
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Zhaoli Liu, Francois A. van Heerden & Zhi-Qiang Wang. (2005) Nodal type bound states of Schrödinger equations via invariant set and minimax methods. Journal of Differential Equations 214:2, pages 358-390.
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Zhitao Zhang. (2004) On bifurcation, critical groups and exact multiplicity of solutions to semilinear elliptic boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 58:5-6, pages 535-546.
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Aixia Qian & Shujie Li. (2004) Multiple nodal solutions for elliptic equations. Nonlinear Analysis: Theory, Methods & Applications 57:4, pages 615-632.
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M. Conti, S. Terracini & G. Verzini. (2002) Nehari's problem and competing species systems. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 19:6, pages 871-888.
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Thomas Bartsch. (2001) Critical Point Theory on Partially Ordered Hilbert Spaces. Journal of Functional Analysis 186:1, pages 117-152.
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Shujie Li & Zhitao Zhang. (2001) Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity. Science in China Series A: Mathematics 44:7, pages 856-866.
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E.N. Dancer & Zhitao Zhang. (2000) Fucik Spectrum, Sign-Changing, and Multiple Solutions for Semilinear Elliptic Boundary Value Problems with Resonance at Infinity. Journal of Mathematical Analysis and Applications 250:2, pages 449-464.
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E.N. Dancer & Yihong Du. (1997) A Note on Multiple Solutions of Some Semilinear Elliptic Problems. Journal of Mathematical Analysis and Applications 211:2, pages 626-640.
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Yihong Du. (1996) Bifurcation from semitrivial solution bundles and applications to certain equation systems. Nonlinear Analysis: Theory, Methods & Applications 27:12, pages 1407-1435.
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