Systems of Kirchhoff type equations with gradient dependence in the reaction term via subsolution-supersolution method

In this paper, we study coupled elliptic systems with gradient dependent right-hand sides and nonlinear boundary conditions, where the left-hand sides are driven by so-called double phase operators. By applying a surjectivity result for pseudomonotone operators along with an equivalent norm in the function space, we prove that the system has at least one nontrivial solution under very general assumptions on the data. Under slightly stronger conditions, we are also able to show that this solution is unique. As a result of independent interest, we further prove the boundedness of solutions to such elliptic systems by employing Moser’s iteration scheme.

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Systems of Kirchhoff type equations with gradient dependence in the reaction term via subsolution-supersolution method

Cited by 6 publications

References 20 publications

Long-time behavior for the Kirchhoff diffusion problem with magnetic fractional Laplace operator

Long-time behavior for the Kirchhoff diffusion problem with magnetic fractional Laplace operator

Multiplicity and concentration properties for (p,q)-Kirchhoff non-autonomous problems with Choquard nonlinearity

Boundedness, existence and uniqueness results for coupled gradient dependent elliptic systems with nonlinear boundary condition

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