superlinear elliptic boundary
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2018 ◽  
Vol 98 (3) ◽  
pp. 465-473 ◽  
Author(s):  
KENTARO HIRATA

We give two-sided estimates for positive solutions of the superlinear elliptic problem$-\unicode[STIX]{x1D6E5}u=a(x)|u|^{p-1}u$with zero Dirichlet boundary condition in a bounded Lipschitz domain. Our result improves the well-knowna priori$L^{\infty }$-estimate and provides information about the boundary decay rate of solutions.



2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Anmin Mao ◽  
Yang Li

Via the Fountain theorem, we obtain the existence of infinitely many solutions of the following superlinear elliptic boundary value problem:−Δu=f(x,u)inΩ,u=0on∂Ω, whereΩ⊂ℝN  (N>2)is a bounded domain with smooth boundary andfis odd inuand continuous. There is no assumption near zero on the behavior of the nonlinearityf, andfdoes not satisfy the Ambrosetti-Rabinowitz type technical condition near infinity.



2006 ◽  
Vol 6 (2) ◽  
Author(s):  
Mónica Clapp ◽  
Eric Hernández-Martínez

AbstractWe study superlinear elliptic boundary value problems with perturbed symmetries in domains which are invariant under the action of a group G. We give conditions on the growth of the nonlinearity which guarantee the existence of infinitely many G-invariant solutions. These conditions improve those obtained by Bahri and Lions (1988) and Bolle, Ghoussoub and Tehrani (2000) if the domain contains a G-orbit of large enough dimension.



1991 ◽  
Vol 34 (3) ◽  
pp. 393-410 ◽  
Author(s):  
L. Päivärinta ◽  
T. Runst

The paper deals with superlinear elliptic boundary value problems depending on a parameter. Given appropriate hypotheses concerning the asymptotic behaviour of the nonlinearity, we prove lower bounds on the number of solutions. The results generalize a theorem due to Lazer and McKenna within the framework of quasi-Banach spaces of Besov and Triebel-Lizorkin spaces.





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