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11.
In 1988, A. Bahri and P.L. Lions [A. Bahri, P.L. Lions, Morse-index of some min–max critical points. I. Application to multiplicity results, Comm. Pure Appl. Math. 41 (1988) 1027–1037] studied the following elliptic problem: where Ω is a bounded smooth domain of , 2<p<(2N−2)/(N−2) and f(x,u) is not assumed to be odd in u. They proved the existence of infinitely many solutions under an appropriate growth restriction on f. In the present paper, we improve this result by showing that under the same growth assumption on f the problem admits in fact infinitely many sign-changing solutions. In addition we derive an estimate on the number of their nodal domains. We also deal with the corresponding fourth order equation Δ2u=|u|p−2u+f(x,u) with both Dirichlet and Navier boundary conditions, as well as with strongly coupled elliptic systems. 相似文献
12.
In this paper, we use the ordinary differential equation theory of Banach spaces and minimax theory, and in particular, the
relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,
and get new multiple solutions and sign-changing solutions theorems, at last we get up to six nontrivial solutions.
Received April 21, 1998, Revised November 2, 1998, Accepted January 14, 1999 相似文献
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Thierry Cazenave Flvio Dickstein Fred B. Weissler 《Journal of Mathematical Analysis and Applications》2009,360(2):537-547
In this paper, we consider the nonlinear heat equation(NLH)
ut−Δu=|u|αu,