Riesz potential, Marcinkiewicz integral and their commutators on mixed Morrey spaces

This paper deals with the boundedness of integral operators and their commutators in the framework of mixed Morrey spaces. Precisely, we study the mixed boundedness of the commutator [b,I?], where I? denotes the fractional integral operator of order ? and b belongs to a suitable homogeneous Lipschitz class. Some results related to the higher order commutator [b,I?]k are also shown. Furthermore, we examine some boundedness properties of the Marcinkiewicz-type integral ?? and the commutator [b,??] when b belongs to the BMO class

Intrinsic square functions and commutators on Morrey-Herz spaces with variable exponents

In this article, we will study the boundedness of intrinsic square functions on the Morrey‐Herz spaces . The boundedness of commutators generated by functions and intrinsic square functions is also discussed on the aforementioned Morrey‐Herz spaces

Positive solutions for (p,2)-equations with superlinear reaction and a concave boundary term

We consider a nonlinear boundary value problem driven by the $(p,2)$-Laplacian, with a $(p-1)$-superlinear reaction and a parametric concave boundary term (a "concave-convex" problem). Using variational tools (critical point theory) together with truncation and comparison techniques, we prove a bifurcation type theorem describing the changes in the set of positive solutions as the parameter $\lambda>0$ varies. We also show that for every admissible parameter $\lambda>0$, the problem has a minimal positive solution $\overline{u}_\lambda$ and determine the monotonicity and continuity properties of the map $\lambda \mapsto \overline{u}_\lambda$

Multiple solutions for Robin ( p , q )-equations plus an indefinite potential and a reaction concave near the origin

AbstractWe consider a Robin problem driven by the (p, q)-Laplacian plus an indefinite potential term. The reaction is either resonant with respect to the principal eigenvalue or$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti-Rabinowitz condition. For both cases we show that the problem has at least five nontrivial smooth solutions ordered and with sign information. When$$q=2$$q=2(a (p, 2)-equation), we show that we can slightly improve the conclusions of the two multiplicity theorems

Constant sign and nodal solutions for parametric (p, 2)-equations

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Homogeneous Herz spaces with variable exponents and regularity results

In this paper we deal with the second order divergence form operators L with coefficients satisfying the vanishing mean oscillation property and we prove some regularity results for a solution to Lu = div f , where f belongs to homogeneous Herz spaces with variable exponents K˙ α,q(·) p(·

Homogeneous Herz spaces with variable exponents and regularity results

In this paper we deal with the second order divergence form operators L with coefficients satisfying the vanishing mean oscillation property and we prove some regularity results for a solution to Lu = div f , where f belongs to homogeneous Herz spaces with variable exponents K˙ α,q(·) p(·

Nonlinear resonant problems with an indefinite potential and concave boundary condition

We consider a nonlinear elliptic problem driven by the p-Laplacian plus and indefinite potential term. The reaction is (p − 1)-linear and resonant and the boundary term is concave. The problem is nonparametric. Using variational tools, together with truncation and perturbation techniques and critical groups, we show that the problem has at least three nontrivial smooth solutions

Positive solutions for (p, 2)-equations with superlinear reaction and a concave boundary term

We consider a nonlinear boundary value problem driven by the (p, 2)- Laplacian, with a (p − 1)-superlinear reaction and a parametric concave boundary term (a “concave-convex” problem). Using variational tools (critical point theory) together with truncation and comparison techniques, we prove a bifurcation type theorem describing the changes in the set of positive solutions as the parameter λ > 0 varies. We also show that for every admissible parameter λ > 0, the problem has a minimal positive solution uλ and determine the monotonicity and continuity properties of the map λ 7→ uλ