arXiv subjects

Maya Chhetri

Publications and source records attributed to Maya Chhetri.

5 recordsLinked to original sources

arXiv2026

On principal eigenpairs for the (p,q)-Laplacian in exterior domain

We consider an eigenvalue problem of the form \begin{equation*} \left\{\begin{array}{rclll} -\Delta_{p} u -\Delta_{q} u&=& \lambda K(x)|u|^{p-2}u & \mbox{ in } \Omega^e u&=&0\qquad \quad &\mbox{ on } \partial \Omega u(x) &\to& 0 &\mbox{ as } |x| \to \infty\,, \end{array}\right. \end{equation*} where $\Omega^e$ is the exterior of a simply connected, bounded domain $\Omega$ in $\mathbb{R}^N$, $p, q \in (1, N)$ with $p \neq q$, $0 < K \in L^{\infty}(\Omega^e) \cap L^{\frac{N}{p}}(\Omega^e)$, and $\lambda \in \mathbb{R}$. We establish the existence of an unbounded set of the principal eigenvalues and corresponding eigenfunctions. Moreover, we establish the regularity, positivity and the asymptotic profiles of these eigenfunctions with respect to the eigenvalue parameter $\lambda$. We use the {\em fibering method} of S.~I. Pohozaev to prove our results.

math.AP↗

arXiv2025

Positive solutions of elliptic systems with superlinear nonlinearities on the boundary

We consider elliptic systems with superlinear and subcritical boundary conditions and a bifurcation parameter as a multiplicative factor. By combining the rescaling method with degree theory and elliptic regularity theory, we prove the existence of a connected branch of positive weak solutions that bifurcates from infinity as the parameter approaches zero. Furthermore, under additional conditions on the nonlinearities near zero, we obtain a global connected branch of positive solutions bifurcating from zero, which possesses a unique bifurcation point from infinity when the parameter is zero. Finally, we analyze the behavior of this branch and discuss the number of positive weak solutions with respect to the parameter using bifurcation theory, degree theory, and sub- and super-solution methods.

math.AP↗

arXiv2025

Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems

We use De Giorgi-Nash-Moser iteration scheme to establish that weak solutions to a coupled system of elliptic equations with critical growth on the boundary are in $L^\infty(\Omega)$. Moreover, we provide an explicit $L^\infty(\Omega)$- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of $H^1(\Omega)$-norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality.

math.AP↗

arXiv2024

An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary

We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition.

math.AP↗

arXiv2021

Bifurcation and Multiplicity Results for Elliptic Problems with Subcritical Nonlinearity on the Boundary

We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation theorem to prove that there exists a connected branch of positive solutions bifurcating from infinity when the parameter goes to zero. Moreover, if the nonlinearity satisfies additional conditions near zero, we establish a global bifurcation result, and discuss the number of positive solution(s) with respect to the parameter using bifurcation theory and degree theory.

math.AP↗