In this paper, we discuss a class of Schrödinger equations involving $p(x)$ -Laplacian-like operators and a convection term. We first establish a novel compact embedding result for variable exponent Sobolev spaces in $\mathbb {R}^{N}$ . Subsequently, by using Galerkin methods in combination with the fixed point theorem and pseudomonotone operators theory, we derive several existence results for various types of solutions, including finite-dimensional approximate solutions, generalized solutions, and weak solutions. Finally, under appropriate assumptions on the nonlinearity, we demonstrate the uniqueness of the weak solution.

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Volume105, Issue5

May 2025

e70066

Existence and uniqueness results for $p(x)$ -Laplacian-like Schrödinger equations with convection term in $\mathbb {R}^{N}$

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Existence and uniqueness results for p ( x ) $p(x)$ -Laplacian-like Schrödinger equations with convection term in R N $\mathbb {R}^{N}$

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Existence and uniqueness results for $p(x)$ -Laplacian-like Schrödinger equations with convection term in $\mathbb {R}^{N}$