On degenerate (p,q)$(p,q)$‐Laplace equations corresponding to an inverse spectral problem

Abstract A method of solving nonlinear boundary value problems involving ‐Laplace with unbounded measurable coefficients is introduced through the inverse optimal problem approach. The existence, uniqueness, and stability of the nonnegative weak solution to the nonlinear equations of the form with unbounded measurable are proven for the first time. An explicit formula that expresses the solution of the nonlinear equations through the inverse optimal solution of the spectral problem is presented. A unique maximizer of the lowest eigenvalue of subject to a constraint in the Lebesgue space is found. Furthermore, a new class of applied problems that lead to equations with ‐Laplace is presented.