Solutions with prescribed mass to Kirchhoff equations: generic double-behaviour nonlinearities
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Date
2025-10-30
Authors
Cai, Li
Radulescu, Vicentiu
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0000-0003-4615-5537Advisor
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Mark
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Abstract
In this paper, we study the Kirchhoff equation {-(a+b integral(3)(R)|del u|(2)dx)Delta u+lambda u=f(u), x is an element of R-3, integral(3)(R)|u|(2)dx=c(2), x is an element of R-3, (lambda,u)is an element of RxH(1)(R-3), where a,b,c>0, lambda is an element of R is unknown as a Lagrange multiplier. We provide generic assumptions about the nonlinearity f(u), which correspond to the L-2-subcritical, L-2-critical, L-2-supercritical, and Sobolev critical cases. Making use of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in L-2(R-3) of radii c, we prove the existence of normalized solutions to the Kirchhoff equation.
In this paper, we study the Kirchhoff equation {-(a+b integral(3)(R)|del u|(2)dx)Delta u+lambda u=f(u), x is an element of R-3, integral(3)(R)|u|(2)dx=c(2), x is an element of R-3, (lambda,u)is an element of RxH(1)(R-3), where a,b,c>0, lambda is an element of R is unknown as a Lagrange multiplier. We provide generic assumptions about the nonlinearity f(u), which correspond to the L-2-subcritical, L-2-critical, L-2-supercritical, and Sobolev critical cases. Making use of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in L-2(R-3) of radii c, we prove the existence of normalized solutions to the Kirchhoff equation.
In this paper, we study the Kirchhoff equation {-(a+b integral(3)(R)|del u|(2)dx)Delta u+lambda u=f(u), x is an element of R-3, integral(3)(R)|u|(2)dx=c(2), x is an element of R-3, (lambda,u)is an element of RxH(1)(R-3), where a,b,c>0, lambda is an element of R is unknown as a Lagrange multiplier. We provide generic assumptions about the nonlinearity f(u), which correspond to the L-2-subcritical, L-2-critical, L-2-supercritical, and Sobolev critical cases. Making use of the minimization of the energy functional over a linear combination of the Nehari and Pohozaev constraints intersected with the product of the closed balls in L-2(R-3) of radii c, we prove the existence of normalized solutions to the Kirchhoff equation.
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Nonlinearity. 2025, vol. 38, issue 10, 33 p.
https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ae0b26
https://iopscience-iop-org.ezproxy.lib.vutbr.cz/article/10.1088/1361-6544/ae0b26
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Peer-reviewed
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en