An application of this compactness result is that problem (1) possesses infinitely many solutions under the same assumptions.
A slenderness parameter is thereby defined based on the elastic local buckling stress of the side wall, idealized as an infinitely long plate under a patch loading transferred from the brace member in combination with a uniform chord pre-load.
Remark 3.2 From the arbitrariness of initial condition ϕ , we know that system (1.6) may in all probability own infinitely many solutions under zero-boundary condition (1.1b).
They proved the existence of at least one solution of (1.1), and the existence of infinitely many solutions under further assumptions.
They obtained that system (1.5) has infinitely many solutions under the assumptions that nonlinear term is superquadratic, asymptotically quadratic and subquadratic, respectively.
By using the variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions, and infinitely many solutions under some different conditions, respectively.
In [1], Ding, Iannacci, and Zanolin showed the existence of 2π-periodic solution and infinitely many subharmonics under the assumptions that (g(x)) is globally Lipschitz and has linear growth at infinity, that is, 0< liminf_{vert xvert to+infty}frac{g(x)}{x}le limsup _{vert xvert to+infty}frac{g(x)}{x}< +infty.
We consider an infinitely large population under stabilizing selection and mutation in which the allelic effects determining a polygenic trait vary between loci.
As an outlook on further research, the calculation of the buckling coefficient for a perforated plate under uniform in-plane compression loading and for an infinitely long perforated plate under shear loading is presented.
The derivation of the solution for the case of infinitely long IDT is under a hypothesis of certain configuration of the IDT wavelength.
