Study on a class of Schrödinger elliptic system involving a nonlinear operator

This paper considers a class of Schrödinger elliptic system involving a nonlinear operator. Firstly, under the simple condition on and ', we prove the existence of the entire positive bounded radial solutions. Secondly, by using the iterative technique and the method of contradiction, we prove the existence and nonexistence of the entire positive blow-up radial solutions. Our results extend the previous existence and nonexistence results for both the single equation and systems. In the end, we give two examples to illustrate our results

Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach

Multiple nonsymmetric nodal solutions for quasilinear Schrödinger system

In this paper, we consider the quasilinear Schrödinger system in RN (N ≥ 3): −∆u + A(x)u − 1 2 ∆(u 2 )u = 2α |u| α−2u|v| −∆v + Bv − 1 2 ∆(v 2 )v = 2β |u| |v| β−2 v, where α, β > 1, 2 0 is a constant. By using a constrained minimization on Nehari–Pohožaev set, for any given integer s ≥ 2, we construct a nonradially symmetrical nodal solution with its 2s nodal domains

Infinitely many periodic solutions for a class of fractional Kirchhoff problems

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of nonlinearities

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp

Multiple and least energy sign-changing solutions for Schrodinger-Poisson equations in R3 with restraint

In this paper, we study the existence of multiple sign-changing solutions with a prescribed Lp+1−norm and theexistence of least energy sign-changing restrained solutions for the following nonlinear Schr¨odinger-Poisson system:By choosing a proper functional restricted on some appropriate subset to using a method of invariant sets of descending flow,we prove that this system has infinitely many sign-changing solutions with the prescribed Lp+1−norm and has a least energy forsuch sign-changing restrained solution for p ∈ (3, 5). Few existence results of multiple sign-changing restrained solutions areavailable in the literature. Our work generalize some results in literature

Multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects

This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result

Existence of positive solutions for a class of p-Laplacian type generalized quasilinear Schrödinger equations with critical growth and potential vanishing at infinity

In this paper, we study the existence of positive solutions for the following generalized quasilinear Schrödinger equation − div(g p (u)|∇u| p−2∇u) + g p−1 (u)g (u)|∇u| p + V(x)|u| p−2u = K(x)f(u) + Q(x)g(u)|G(u)| p ∗−2G(u), x ∈ R N, where N ≥ 3, 1 < p ≤ N, p Np N−p , g ∈ C1 (R, R+), V(x) and K(x) are positive continuous functions and G(u) = R u 0 g(t)dt. By using a change of variable, we obtain the existence of positive solutions for this problem by using the Mountain Pass Theorem. Our results generalize some existing results