LAPLACIAN operatorWe prove the existence of a positive solution to the $ (p, q) $ Laplacian problem$ \\begin{equation*} \\left\\{ \\begin{array}{c} -\\Delta _{p}u-\\Delta _{q}u=\\lambda f(u)\\ ext{ in }\\Omega ,
Thanks to the proposition above, we can get the following positive answer to in p-sublinear case.Theorem 1.6Let andΩ be class of . Assume that a.e. inΩ. Then, defined in (1.7) is attained and is the second eigenvalue, that is, ...
Recently, convergence problems of various generalizations of classical Hermite-Padé approximants on row sequences were considered in [13–16]. The results in [16] generalize the ones in [8] to MHP approximants. In particular, Bosuwan et al. [16] computed the exact rate of convergence of {...
p-LaplacianSublinear perturbationIndefinite weightAntimaximum principleMaximum principleHarnack inequalityPicone inequalityExistenceLinking method35J92We investigate qualitative properties of weak solutions of the Dirichlet problem for the equation -Δpu=λm(x)|u|p-2u+ηa(x)|u|q-2u+f(x)documentclass[12...
In harmonic analysis, there is a large interest in the study of the properties of singular integral operators. Our starting point is the well-known fact that the Hilbert transform Hγf(x)=p.v.1∫−1f(x−γ(t))dtt,Hγf(x)=p.v.∫−11f(x−γ(t))dtt, where γ:(−1...
On a sublinear Robin equations involving $$\\mu (x)$$ -Laplacian with small perturbationdoi:10.1007/s10998-024-00623-zVariable exponentsRobin conditionvariational methodsThe present paper deals with the existence of solutions for Robin equations with variable exponents. In particular, we suppose that...