Singular Anisotropic Double Phase Problems

Article Mathematics

The Nehari manifold approach for singular equations involving the p(x)-Laplace operator

Dusan D. Repovs et al.

Summary: This study investigates a singular problem involving the p(x)-Laplace operator, and applies the Nehari manifold approach and new techniques to establish the multiplicity of positive solutions for the problem.

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS (2023)

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Article Mathematics, Applied

Anisotropic Dirichlet double phase problems with competing nonlinearities

S. Leonardi et al.

Summary: This article considers a Dirichlet double phase problem with variable exponents and nonstandard growth. The reaction has the competing effects of a parametric concave term and a superlinear perturbation, resulting in a concave-convex problem. It is shown that for all small values of the parameter, the problem has at least two nontrivial bounded solutions.

REVISTA MATEMATICA COMPLUTENSE (2023)

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Article Mathematics, Applied

On the local behavior of local weak solutions to some singular anisotropic elliptic equations

Simone Ciani et al.

Summary: In this study, we investigate the local behavior of bounded local weak solutions to a class of anisotropic singular equations. By using a parabolic approach to expand positivity, we obtain the interior Holder continuity and some integral and pointwise Harnack inequalities.

ADVANCES IN NONLINEAR ANALYSIS (2023)

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Article Mathematics

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN (p, q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

Salvatore Leonardi et al.

Summary: In this paper, we consider a nonlinear Robin problem driven by the (p, q)-Laplacian and with an indefinite potential term as well as a parametric reaction term. Under minimal conditions on the behavior of the reaction function near zero, we prove the existence of a nodal solution ylambda∈C-l((Ω) over bar) for all small positive lambda, and we also show that ylambda converges to zero in C-l((Ω) over bar) as lambda approaches 0(+).

ACTA MATHEMATICA SCIENTIA (2022)

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Article Mathematics, Applied

Singular quasilinear convective elliptic systems in Double-struck capital RN

Umberto Guarnotta et al.

Summary: This paper establishes the existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms, primarily through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity results are then used to show that the obtained solution is actually strong.

ADVANCES IN NONLINEAR ANALYSIS (2022)

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Article Mathematics, Applied

ANISOTROPIC SINGULAR DOUBLE PHASE DIRICHLET PROBLEMS

Nikolaos S. Papageorgiou et al.

Summary: This study examines an anisotropic double phase problem with a reaction, involving the competing effects of a parametric singular term and a superlinear perturbation. By utilizing variational tools, truncation and comparison techniques, as well as general results on anisotropic equations, the changes in the set of positive solutions as the parameter varies on R+ = (0, +infinity) are described through a bifurcation-type result.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S (2021)

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Article Mathematics