Existence and Uniqueness of Weak solution of $p( x )$ - laplacian in Sobolev spaces with variable exponents in complete manifolds

preprint2020arXivOpen access

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous $p ( x ) -$ laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian manifolds. The mountain pass Theorem is used.

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Existence and Uniqueness of Weak solution of $p( x )$ - laplacian in Sobolev spaces with variable exponents in complete manifolds

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Existence and Uniqueness of Weak solution of p(x) p( x ) p(x)- laplacian in Sobolev spaces with variable exponents in complete manifolds

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Existence and Uniqueness of Weak solution of $p( x )$ - laplacian in Sobolev spaces with variable exponents in complete manifolds