Multiple solutions for a semilinear boundary value problem: A computational multiplicity proof
type: Item
instance of: scholarly article
title: Multiple solutions for a semilinear boundary value problem: A computational multiplicity proof
zbMATH Open document ID: 0973.35080
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-11-27T00:00:00Z
review text: In the paper there is with unstandard advance proved the following theorem: Let \(\Omega= (0,1)\times(0,1)\). The boundary value problem \[ \Delta u= u^2= s\sin\pi x\cdot\sin\pi y\quad\text{in }\Omega, \] \[ u|_{\partial\Omega}= 0, \] has at least four solutions for \(s= 800\).
reviewed by: Rudolf Kodnár
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1556940
zbMATH Keywords: nonlinear problem
zbMATH Keywords: multiple solution
zbMATH Keywords: fixed point
author: P. Joseph Mckenna
author: Michael Plum
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7039
OpenAlex ID: W2079396610
cites work: On the inversion of some differentiable mappings with singularities between Banach spaces
cites work: Q4320844
cites work: Radially Symmetric Solutions to a Superlinear Dirichlet Problem in a Ball With Jumping Nonlinearities
cites work: The exact number of solutions for a class of ordinary differential equations through Morse index computation
cites work: A mountain pass method for the numerical solution of semilinear elliptic problems
cites work: A mountain pass method for the numerical solution of semilinear wave equations
cites work: Counterexamples to some conjectures on the number of solutions of nonlinear equations
cites work: Degenerate critical points, homotopy indices and Morse inequalities.
cites work: A counterexample to the Lazer–McKenna conjecture
cites work: Variational and topological methods in partially ordered Hilbert spaces
cites work: On the unboundedness of the number of solutions of a Dirichlet problem
cites work: Remarks on some quasilinear elliptic equations
cites work: On the number of solutions of a nonlinear Dirichlet problem
cites work: Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
cites work: On a conjecture related to the number of solutions of a nonlinear Dirichlet problem
cites work: A symmetry theorem and applications to nonlinear partial differential equations
cites work: Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
cites work: Q4350124
cites work: Bounds for eigenvalues of second-order elliptic differential operators
cites work: Q3749777
cites work: On a Class of Superlinear Sturm–Liouville Problems with Arbitrarily Many Solutions
cites work: Some remarks on the number of solutions of some nonlinear elliptic problems
DOI: 10.1006/JMAA.2000.7039
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description: scientific article; zbMATH DE number 1556940