Sentence examples for more general nonlinearity from inspiring English sources

Gupta [1] and Yao [4] studied the problem with more general nonlinearity but established existence results only.

Zhang [6] proved the existence of solutions for a more general nonlinearity (f x,u)) under some weaker assumptions.

In [3], Micheletti and Pistoia used a variational linking theorem to investigate the existence of two solutions for a more general nonlinearity (g(cdot,u)).

Later, Bognara and Drabekb [29] deals with the existence and multiplicity results for radial symmetric solutions of problem (1.1) for a more general nonlinearity (g u)).

In Ouyang and Shi [7, 8], their result classified the different global exact multiplicity of (1.3) for more general nonlinearity f.

For problem (1) when (f x,u =bg x,u)), Micheletti and Pistoia [4] proved that there exist two or three solutions for a more general nonlinearity g by the variational method.

Instead of the cubic term, more general nonlinearities can be considered as well.

There is ongoing research in our group to establish similar results for more general nonlinearities [40].

In this section, we consider (1.1) with α = 1 and more general nonlinearities f satisfying condition (A).

Among the reference works mentioned above, Hai and Shivaji [17] and Ali and Shivaji [2] (with more general nonlinearities) considered problem ( P E ) with case k i ≡ 1 and Ω bounded.

(gin Sigma )) attractors in different kinds of phase spaces for equations analogous to equation (1.1) ((varepsilon =0) or (varepsilon >0)) with more general nonlinearities and external forces have been investigated in many literature works (see, e.g., [9, 14 18] and the references therein).