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MULTIPLICITY OF NORMALIZED SOLUTIONS FOR NONLINEAR KIRCHHOFF-TYPE PROBLEMS
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DOI：10.1007/s10473-026-0311-2.png)
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Abstract
En 中文
This paper addresses the existence of multiple nonradial and radial normalized solutions for the following Kirchhoff-type equations { -(a + b integral(RN) |del u|(2)dx)Delta u = f (u) - mu u in R-N, ||u||(L2(RN)) = m , u is an element of H-1 (R-N), where f is an element of C(R, R), a, b > 0 are constants, mu is an element of R is not fixed and instead appears as a Lagrange multiplier and m > 0 is a given constant. In a mass subcritical case, using a version of the minimax theorem ([32, Theorem 2.1]) for a class of constrained even functionals, we demonstrate the existence of one nonradial normalized solution when N >= 4. Additionally, if N >= 4 and N not equal 5, we obtain multiple nonradial normalized solutions. Moreover, the existence of infinitely many radial normalized solutions is explored for N >= 2. Furthermore, all solutions discussed above are sign-changing. As a supplementary result, we also prove the nonexistence of nontrivial solutions. Lastly, we analyze the asymptotic behavior of all solutions obtained above as b -> 0.
Keywords:
Kirchhoff-type equations
multiple nonradial and radial normalized solutions
sign-changing solutions
asymptotic behavior
Journal
A
IF:
1.1
Papers:
93
Citations:
0