Weak solutions for double phase problem driven by the (p(x),q(x))-Laplacian operator under Dirichlet boundary conditions
Copyright policy )Weak solutions for double phase problem driven by the (p(x),q(x))-Laplacian operator under Dirichlet boundary conditions
In the present paper, in view of the topological degree methods and the theory of the variable exponent Sobolev spaces, we discuss a Dirichlet boundary value problem for elliptic equations involving the $(p(x),q(x))$-Laplacian operator with a reaction term depending on the gradient and on two real parameters. Under certain assumptions, we establish the existence of at least one weak solution to this problem. Our results extends some recent work in the literature.
Inverse Problems in Mathematical Physics and Imaging, Dirichlet distribution, topological degree methods, Biochemistry, Gene, Term (time), Fractional Laplacian Operators, Variable (mathematics), Boundary value problem, Mathematical Physics, Dirichlet problem, double phase problem, Applied Mathematics, Physics, Elliptic boundary value problem, Elliptic Problems, FOS: Philosophy, ethics and religion, Elliptic operator, Chemistry, Computational Theory and Mathematics, Laplace operator, Mixed boundary condition, Physical Sciences, \((p(x),q(x))\)-Laplacian operators, Degenerate elliptic equations, Nonlinear elliptic equations, Operator (biology), Mathematical analysis, Quantum mechanics, QA1-939, FOS: Mathematics, Multiscale Methods for Heterogeneous Systems, Elliptic Equations, Weak solutions to PDEs, Degree (music), Quasilinear elliptic equations with \(p\)-Laplacian, Degree theory for nonlinear operators, Exponent, p-Laplacian, Pure mathematics, variable exponent Sobolev spaces, Linguistics, Acoustics, Sobolev space, Philosophy, Boundary Value Problems, Boundary (topology), Computer Science, FOS: Languages and literature, Repressor, Transcription factor, Mathematics
Inverse Problems in Mathematical Physics and Imaging, Dirichlet distribution, topological degree methods, Biochemistry, Gene, Term (time), Fractional Laplacian Operators, Variable (mathematics), Boundary value problem, Mathematical Physics, Dirichlet problem, double phase problem, Applied Mathematics, Physics, Elliptic boundary value problem, Elliptic Problems, FOS: Philosophy, ethics and religion, Elliptic operator, Chemistry, Computational Theory and Mathematics, Laplace operator, Mixed boundary condition, Physical Sciences, \((p(x),q(x))\)-Laplacian operators, Degenerate elliptic equations, Nonlinear elliptic equations, Operator (biology), Mathematical analysis, Quantum mechanics, QA1-939, FOS: Mathematics, Multiscale Methods for Heterogeneous Systems, Elliptic Equations, Weak solutions to PDEs, Degree (music), Quasilinear elliptic equations with \(p\)-Laplacian, Degree theory for nonlinear operators, Exponent, p-Laplacian, Pure mathematics, variable exponent Sobolev spaces, Linguistics, Acoustics, Sobolev space, Philosophy, Boundary Value Problems, Boundary (topology), Computer Science, FOS: Languages and literature, Repressor, Transcription factor, Mathematics
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