Existence of Solutions for Sublinear Kirchhoff Problems with Sublinear Growth

Characterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion

In this paper we characterize the existence of large solutions for a general class of sublinear elliptic problems of logistic type related to the porous media equation. Our main result shows that large solutions do exist if, and only if, the nonlinear diffusion is not too large. As a byproduct of the general theory developed by the authors in [2], those large solutions must be unstable with res...

A note on the existence and multiplicity of solutions for sublinear fractional problems

On the Existence of Positive Solutions for Periodic Parabolic Sublinear Problems

Similarly, let L p T be the Banach space ofT-periodic functions f such that f |Ω×(0,T) ∈ Lp(Ω× (0,T)), equipped with the norm ‖ f ‖Lp T := ‖ f |Ω×(0,T)‖Lp(Ω×(0,T)). Finally, let CT be the space of continuous and T-periodic functions onΩ×R provided with the L∞-norm. For the whole paper, we fix v,s ∈ (1,∞] such that N/2v + 1/s < 1, s > 2. Let {ai j} and {bj}, 1 ≤ i, j ≤ N , be two families of fun...

Boundedness of solutions for sublinear reversible systems

In this paper we will study the boundedness of all solutions for second-order differential equations ẍ+ f(x)ẋ+ λx+ g(x) = p(t), where λ ∈ R and g(x) satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence...

Exact multiplicity of solutions to superlinear and sublinear problems

(f2) lim u→∞ f(u) u =f+ ¿ 0; lim u→−∞ f(u) u =f− ¿ 0: For the de5niteness, we assume f+ ¿f−, and when f+ =f−, we use f± to represent it. We will consider f being either superlinear or sublinear. f is said to be superlinear if f(u)=u is decreasing in (0;∞) and is increasing in (−∞; 0); and f is said to be sublinear if f(u)=u is increasing in (0;∞) and is decreasing in (−∞; 0): The semilinear equ...