Nontrivial Solutions for Periodic Schrödinger Equations with Sign-Changing Nonlinearities

Existence of Nontrivial Solutions for Singular Quasilinear Equations with Sign Changing Nonlinearity

By an application of Bonanno’s three critical point theorem, we establish the existence of a nontrivial solution to the problem −∆pu = μ g(x)|u|p−2u |x|p + λa(x)f(u) in Ω, u = 0 on ∂Ω, under some restrictions on g, a and f for certain positive values of μ and λ.

Multiple Positive Solutions for Singular Elliptic Equations with Concave-Convex Nonlinearities and Sign-Changing Weights

Recommended by Pavel Drabek We study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu − μ/|x| 2 u λfx|u| q−2 u gx|u| 2 * −2 u in Ω, u 0 on ∂Ω, where 0 ∈ Ω ⊂ R N N ≥ 3 is a bounded domain with smooth boundary ∂Ω, λ > 0, 0 ≤ μ < μ N − 2 2 /4, 2 * 2N/N − 2, 1 ≤ q < 2, and f, g are continuous functions on Ω which are somewhere positive but which may change...

Existence and multiplicity of nontrivial solutions for‎ ‎$p$-Laplacian system with nonlinearities of concave-convex type and‎ ‎sign-changing weight functions

This paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎With the help of the Nehari manifold and Palais-Smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a c...

Damped vibration problems with sign-changing nonlinearities: infinitely many periodic solutions

IN×N is theN×N identity matrix, q(t) ∈ L(R;R) is T-periodic and satisfies ∫ T  q(t)dt = , A(t) = [aij(t)] is aT-periodic symmetricN×N matrix-valued functionwith aij ∈ L∞(R;R) (∀i, j = , , . . . ,N ), B = [bij] is an antisymmetric N × N constant matrix, u = u(t) ∈ C(R,RN ), H(t,u) ∈ C(R × RN ,R) is T-periodic and Hu(t,u) denotes its gradient with respect to the u variable. In fact, there ...

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations