In this paper, by using critical point theory, we obtain some sufficient conditions on the existence of infinitely many positive solutions of the boundary value problems for a second-order ...ϕc-Laplacian difference equation. To the best of our knowledge, this is the first time to discuss the existence of infinitely many positive solutions to the boundary value problems for difference equations involving the special ϕc-Laplacian operator.
In this paper we establish the existence, non-existence and multiplicity of solutions for a class of generalized Schrödinger–Bopp–Podolsky system with singular nonlinearity. The main techniques we ...use are some results on critical point theory for non-differentiable functionals and the sub-supersolution method.
In this paper we prove the existence of a radial ground state solution for a quasilinear problem involving the mean curvature operator in Minkowski space.
In this study, the following nonlinear magnetic Schrödinger equation is considered−ΔAu+V(x)u=Eu+|u|p−2u,x=(x1,x2)∈R2, where 2<p<+∞, A(x)=(0,−b(x1)), b(x1)=∫0x1B(t)dt, B∈C∞(R,R) is an increasing ...function with different limits at +∞ and −∞. Under these assumptions, the magnetic Laplacian operator −ΔA is known as an Iwatsuka model, and its spectrum has a band structure. In addition, E is an edge of a spectral gap of operator −ΔA, and V is a power-like decay potential. It is proved that this equation has a sequence of non-zero solutions, whose L∞ norms tend to zero along this sequence. The proof is given by establishing a new critical point theorem without the usual (PS)⁎ condition. This study is a subsequent work to a recent one (Chen, 2022 11).
In this paper, by using Leray–Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C1-functionals, we obtain existence of classical positive radial ...solutions for Dirichlet problems of typediv(∇v1−|∇v|2)+f(|x|,v)=0in B(R),v=0on ∂B(R). Here, B(R)={x∈RN:|x|<R} and f:0,R×0,α)→R is a continuous function, which is positive on (0,R×(0,α).
We study a pseudo-differential equation driven by the degenerate fractional p-Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order ...interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques.
In this paper, we consider the following magnetic Schrödinger equation−ΔAu+V(x)u=Enu+|u|p−2u,x∈R2, where 2<p<∞, A(x)=(bx22,−bx12), x=(x1,x2)∈R2, En is an eigenvalue of −ΔA with infinitely ...multiplicity, and V is a non-zero and nonnegative function in Lp/(p−2)(R2,R). We prove that this equation has a sequence of non-zero solutions whose L∞ norms tend to zero along this sequence. To prove this, a new critical point theorem without the Palais-Smale condition is established.
By using critical point theory, we obtain some new sufficient conditions for the existence of homoclinic solutions of discrete prescribed mean curvature equations with mixed nonlinearities for the ...unbounded potentials. To the best of our knowledge, there are no results on the existence of infinitely many homoclinic solutions to difference equations with mixed nonlinearities in the existing literature.
In this paper we consider a class of logarithmic Schrödinger equations with a potential which may change sign. When the potential is coercive, we obtain infinitely many solutions by adapting some ...arguments of the Fountain theorem, and in the case of bounded potential we obtain a ground state solution, i.e. a nontrivial solution with least possible energy. The functional corresponding to the problem is the sum of a smooth and a convex lower semicontinuous term.
By using critical point theory, the existence of heteroclinic solutions for a second-order difference equation involving the mean curvature operator is obtained, and the values of solutions at −∞ and ...+∞ are more general than existing results in the literature. An example is presented to demonstrate the applicability of our main results.
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